Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520617009295/xk5041sup1.cif | |
Portable Document Format (PDF) file https://doi.org/10.1107/S2052520617009295/xk5041sup22.pdf | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_100sup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_150sup3.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_200sup4.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_250sup5.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_280sup6.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_299sup7.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_320sup8.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_330sup9.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_340sup10.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_350sup11.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_360sup12.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_370sup13.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_380sup14.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_390sup15.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_400sup16.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_420sup17.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_440sup18.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_460sup19.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_480sup20.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520617009295/xk5041norse_500sup21.hkl |
CCDC references: 1557350; 1557351; 1557352; 1557353; 1557354; 1557355; 1557356; 1557357; 1557358; 1557359; 1557360; 1557361; 1557362; 1557363; 1557364; 1557365; 1557366; 1557367; 1557368; 1567750
For all structures, program(s) used to refine structure: SHELXL2014/7 (Sheldrick, 2014).
C6Ba3Mg3O18 | Dx = 3.868 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9285 reflections |
a = 5.0083 (1) Å | θ = 1.5–45° |
c = 33.3987 (8) Å | µ = 8.30 mm−1 |
V = 725.51 (3) Å3 | T = 100 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.030 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9285 measured reflections | k = −10→9 |
692 independent reflections | l = −65→34 |
535 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.012P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.021 | (Δ/σ)max < 0.001 |
S = 1.01 | Δρmax = 0.54 e Å−3 |
692 reflections | Δρmin = −0.58 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.00471 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00457 (7) | |
O3 | 0.11020 (13) | 0.81779 (13) | 0.12928 (2) | 0.00912 (9) | |
C4 | 0.0000 | 0.0000 | 0.13043 (3) | 0.00515 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00405 (2) | 0.00405 (2) | 0.00603 (3) | 0.00203 (1) | 0.000 | 0.000 |
Mg2 | 0.00406 (11) | 0.00406 (11) | 0.00558 (16) | 0.00203 (5) | 0.000 | 0.000 |
O3 | 0.0118 (2) | 0.0095 (2) | 0.01034 (17) | 0.0085 (2) | −0.00348 (15) | −0.00195 (14) |
C4 | 0.00497 (17) | 0.00497 (17) | 0.0055 (2) | 0.00248 (8) | 0.000 | 0.000 |
Ba1—O3i | 2.7904 (5) | Mg2—O3xviii | 2.0558 (6) |
Ba1—O3ii | 2.7904 (5) | Mg2—Ba1xix | 4.0135 (1) |
Ba1—O3iii | 2.7904 (6) | Mg2—Ba1xx | 4.0135 (1) |
Ba1—O3iv | 2.7904 (6) | Mg2—Ba1xxi | 4.0135 (1) |
Ba1—O3v | 2.7904 (5) | Mg2—Ba1xxii | 4.0135 (1) |
Ba1—O3vi | 2.7904 (5) | Mg2—Ba1iii | 4.0135 (1) |
Ba1—O3vii | 3.0971 (6) | Mg2—Ba1xxiii | 4.0135 (1) |
Ba1—O3viii | 3.0971 (6) | O3—C4xxiv | 1.2816 (6) |
Ba1—O3ix | 3.0972 (6) | O3—Mg2xxv | 2.0559 (6) |
Ba1—O3x | 3.0972 (6) | O3—Ba1iii | 2.7904 (5) |
Ba1—O3xi | 3.0972 (6) | O3—Ba1x | 3.0972 (6) |
Ba1—O3xii | 3.0972 (6) | C4—O3xxvi | 1.2816 (6) |
Mg2—O3xiii | 2.0558 (6) | C4—O3xxvii | 1.2816 (6) |
Mg2—O3xiv | 2.0558 (6) | C4—O3xxviii | 1.2816 (6) |
Mg2—O3xv | 2.0558 (6) | C4—Ba1xxi | 3.2916 (4) |
Mg2—O3xvi | 2.0558 (6) | C4—Ba1xx | 3.2916 (4) |
Mg2—O3xvii | 2.0558 (6) | C4—Ba1iii | 3.2916 (4) |
O3i—Ba1—O3ii | 123.74 (2) | O3xiv—Mg2—O3xviii | 86.95 (2) |
O3i—Ba1—O3iii | 137.64 (2) | O3xv—Mg2—O3xviii | 93.05 (2) |
O3ii—Ba1—O3iii | 92.660 (17) | O3xvi—Mg2—O3xviii | 86.95 (2) |
O3i—Ba1—O3iv | 92.660 (17) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 137.64 (2) | O3xiii—Mg2—Ba1xix | 40.505 (15) |
O3iii—Ba1—O3iv | 67.23 (2) | O3xiv—Mg2—Ba1xix | 139.495 (15) |
O3i—Ba1—O3v | 92.659 (17) | O3xv—Mg2—Ba1xix | 49.391 (16) |
O3ii—Ba1—O3v | 67.23 (2) | O3xvi—Mg2—Ba1xix | 130.609 (16) |
O3iii—Ba1—O3v | 123.74 (2) | O3xvii—Mg2—Ba1xix | 98.493 (17) |
O3iv—Ba1—O3v | 92.658 (17) | O3xviii—Mg2—Ba1xix | 81.507 (17) |
O3i—Ba1—O3vi | 67.23 (2) | O3xiii—Mg2—Ba1xx | 139.495 (15) |
O3ii—Ba1—O3vi | 92.659 (17) | O3xiv—Mg2—Ba1xx | 40.505 (15) |
O3iii—Ba1—O3vi | 92.658 (17) | O3xv—Mg2—Ba1xx | 130.609 (16) |
O3iv—Ba1—O3vi | 123.74 (2) | O3xvi—Mg2—Ba1xx | 49.391 (16) |
O3v—Ba1—O3vi | 137.64 (2) | O3xvii—Mg2—Ba1xx | 81.507 (17) |
O3i—Ba1—O3vii | 176.304 (11) | O3xviii—Mg2—Ba1xx | 98.493 (17) |
O3ii—Ba1—O3vii | 57.15 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.90 (2) | O3xiii—Mg2—Ba1xxi | 81.507 (17) |
O3iv—Ba1—O3vii | 85.188 (13) | O3xiv—Mg2—Ba1xxi | 98.493 (17) |
O3v—Ba1—O3vii | 84.451 (13) | O3xv—Mg2—Ba1xxi | 139.494 (15) |
O3vi—Ba1—O3vii | 116.470 (19) | O3xvi—Mg2—Ba1xxi | 40.506 (15) |
O3i—Ba1—O3viii | 57.15 (2) | O3xvii—Mg2—Ba1xxi | 130.609 (16) |
O3ii—Ba1—O3viii | 176.304 (11) | O3xviii—Mg2—Ba1xxi | 49.391 (16) |
O3iii—Ba1—O3viii | 85.188 (13) | Ba1xix—Mg2—Ba1xxi | 102.791 (1) |
O3iv—Ba1—O3viii | 43.90 (2) | Ba1xx—Mg2—Ba1xxi | 77.209 (1) |
O3v—Ba1—O3viii | 116.470 (19) | O3xiii—Mg2—Ba1xxii | 98.493 (17) |
O3vi—Ba1—O3viii | 84.451 (13) | O3xiv—Mg2—Ba1xxii | 81.507 (17) |
O3vii—Ba1—O3viii | 122.24 (2) | O3xv—Mg2—Ba1xxii | 40.506 (15) |
O3i—Ba1—O3ix | 43.90 (2) | O3xvi—Mg2—Ba1xxii | 139.494 (15) |
O3ii—Ba1—O3ix | 84.450 (13) | O3xvii—Mg2—Ba1xxii | 49.391 (16) |
O3iii—Ba1—O3ix | 176.304 (12) | O3xviii—Mg2—Ba1xxii | 130.609 (16) |
O3iv—Ba1—O3ix | 116.470 (19) | Ba1xix—Mg2—Ba1xxii | 77.209 (1) |
O3v—Ba1—O3ix | 57.15 (2) | Ba1xx—Mg2—Ba1xxii | 102.791 (1) |
O3vi—Ba1—O3ix | 85.190 (13) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 134.87 (2) | O3xiii—Mg2—Ba1iii | 130.609 (16) |
O3viii—Ba1—O3ix | 97.574 (13) | O3xiv—Mg2—Ba1iii | 49.391 (16) |
O3i—Ba1—O3x | 84.450 (13) | O3xv—Mg2—Ba1iii | 81.507 (16) |
O3ii—Ba1—O3x | 43.90 (2) | O3xvi—Mg2—Ba1iii | 98.493 (16) |
O3iii—Ba1—O3x | 116.470 (19) | O3xvii—Mg2—Ba1iii | 139.495 (15) |
O3iv—Ba1—O3x | 176.304 (12) | O3xviii—Mg2—Ba1iii | 40.506 (15) |
O3v—Ba1—O3x | 85.190 (13) | Ba1xix—Mg2—Ba1iii | 102.791 (1) |
O3vi—Ba1—O3x | 57.15 (2) | Ba1xx—Mg2—Ba1iii | 77.209 (1) |
O3vii—Ba1—O3x | 97.574 (13) | Ba1xxi—Mg2—Ba1iii | 77.209 (1) |
O3viii—Ba1—O3x | 134.87 (2) | Ba1xxii—Mg2—Ba1iii | 102.791 (1) |
O3ix—Ba1—O3x | 59.83 (2) | O3xiii—Mg2—Ba1xxiii | 49.391 (16) |
O3i—Ba1—O3xi | 85.189 (13) | O3xiv—Mg2—Ba1xxiii | 130.609 (16) |
O3ii—Ba1—O3xi | 116.470 (19) | O3xv—Mg2—Ba1xxiii | 98.493 (16) |
O3iii—Ba1—O3xi | 57.15 (2) | O3xvi—Mg2—Ba1xxiii | 81.507 (16) |
O3iv—Ba1—O3xi | 84.452 (13) | O3xvii—Mg2—Ba1xxiii | 40.506 (15) |
O3v—Ba1—O3xi | 176.304 (12) | O3xviii—Mg2—Ba1xxiii | 139.495 (15) |
O3vi—Ba1—O3xi | 43.89 (2) | Ba1xix—Mg2—Ba1xxiii | 77.209 (1) |
O3vii—Ba1—O3xi | 97.574 (13) | Ba1xx—Mg2—Ba1xxiii | 102.791 (1) |
O3viii—Ba1—O3xi | 59.83 (2) | Ba1xxi—Mg2—Ba1xxiii | 102.791 (1) |
O3ix—Ba1—O3xi | 122.24 (2) | Ba1xxii—Mg2—Ba1xxiii | 77.209 (1) |
O3x—Ba1—O3xi | 97.573 (13) | Ba1iii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.470 (19) | C4xxiv—O3—Mg2xxv | 138.67 (5) |
O3ii—Ba1—O3xii | 85.189 (13) | C4xxiv—O3—Ba1iii | 101.33 (4) |
O3iii—Ba1—O3xii | 84.452 (13) | Mg2xxv—O3—Ba1iii | 110.90 (2) |
O3iv—Ba1—O3xii | 57.15 (2) | C4xxiv—O3—Ba1x | 87.11 (3) |
O3v—Ba1—O3xii | 43.89 (2) | Mg2xxv—O3—Ba1x | 100.35 (2) |
O3vi—Ba1—O3xii | 176.304 (12) | Ba1iii—O3—Ba1x | 116.471 (19) |
O3vii—Ba1—O3xii | 59.83 (2) | O3xxvi—C4—O3xxvii | 119.913 (5) |
O3viii—Ba1—O3xii | 97.574 (13) | O3xxvi—C4—O3xxviii | 119.911 (5) |
O3ix—Ba1—O3xii | 97.573 (13) | O3xxvii—C4—O3xxviii | 119.911 (5) |
O3x—Ba1—O3xii | 122.24 (2) | O3xxvi—C4—Ba1xxi | 70.01 (3) |
O3xi—Ba1—O3xii | 134.87 (2) | O3xxvii—C4—Ba1xxi | 148.77 (6) |
O3xiii—Mg2—O3xiv | 180.00 (4) | O3xxviii—C4—Ba1xxi | 56.22 (3) |
O3xiii—Mg2—O3xv | 86.95 (2) | O3xxvi—C4—Ba1xx | 148.77 (6) |
O3xiv—Mg2—O3xv | 93.05 (2) | O3xxvii—C4—Ba1xx | 56.22 (3) |
O3xiii—Mg2—O3xvi | 93.05 (2) | O3xxviii—C4—Ba1xx | 70.01 (3) |
O3xiv—Mg2—O3xvi | 86.95 (2) | Ba1xxi—C4—Ba1xx | 99.066 (18) |
O3xv—Mg2—O3xvi | 180.00 (4) | O3xxvi—C4—Ba1iii | 56.22 (3) |
O3xiii—Mg2—O3xvii | 86.95 (2) | O3xxvii—C4—Ba1iii | 70.01 (3) |
O3xiv—Mg2—O3xvii | 93.05 (2) | O3xxviii—C4—Ba1iii | 148.77 (6) |
O3xv—Mg2—O3xvii | 86.95 (2) | Ba1xxi—C4—Ba1iii | 99.065 (18) |
O3xvi—Mg2—O3xvii | 93.05 (2) | Ba1xx—C4—Ba1iii | 99.065 (18) |
O3xiii—Mg2—O3xviii | 93.05 (2) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) x−1/3, x−y+1/3, z−1/6; (xiv) −x+1/3, −x+y−1/3, −z+1/6; (xv) −y+2/3, −x+1/3, z−1/6; (xvi) y−2/3, x−1/3, −z+1/6; (xvii) −x+y−1/3, y−2/3, z−1/6; (xviii) x−y+1/3, −y+2/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) −x−1/3, −y−2/3, −z+1/3; (xxii) x+1/3, y+2/3, z−1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −x+y−1, −x, z; (xxvii) −y+1, x−y+1, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.869 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 8758 reflections |
a = 5.0084 (2) Å | θ = 1.5–45° |
c = 33.3941 (15) Å | µ = 8.30 mm−1 |
V = 725.43 (7) Å3 | T = 150 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.030 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
8758 measured reflections | k = −10→9 |
692 independent reflections | l = −65→34 |
506 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0096P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.020 | (Δ/σ)max < 0.001 |
S = 1.02 | Δρmax = 0.42 e Å−3 |
692 reflections | Δρmin = −0.58 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.00611 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00530 (7) | |
O3 | 0.11154 (14) | 0.81907 (14) | 0.12925 (2) | 0.01115 (11) | |
C4 | 0.0000 | 0.0000 | 0.13038 (3) | 0.00599 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00533 (2) | 0.00533 (2) | 0.00767 (3) | 0.00267 (1) | 0.000 | 0.000 |
Mg2 | 0.00471 (10) | 0.00471 (10) | 0.00650 (17) | 0.00235 (5) | 0.000 | 0.000 |
O3 | 0.0149 (3) | 0.0119 (3) | 0.01229 (18) | 0.0109 (3) | −0.00434 (17) | −0.00267 (16) |
C4 | 0.00584 (17) | 0.00584 (17) | 0.0063 (3) | 0.00292 (8) | 0.000 | 0.000 |
Ba1—O3i | 2.7952 (6) | Mg2—O3xviii | 2.0556 (6) |
Ba1—O3ii | 2.7952 (6) | Mg2—Ba1xix | 4.0132 (1) |
Ba1—O3iii | 2.7952 (6) | Mg2—Ba1xx | 4.0132 (1) |
Ba1—O3iv | 2.7952 (6) | Mg2—Ba1xxi | 4.0132 (1) |
Ba1—O3v | 2.7952 (6) | Mg2—Ba1xxii | 4.0132 (1) |
Ba1—O3vi | 2.7952 (6) | Mg2—Ba1xxiii | 4.0133 (1) |
Ba1—O3vii | 3.0909 (6) | Mg2—Ba1iii | 4.0133 (1) |
Ba1—O3viii | 3.0909 (6) | O3—C4xxiv | 1.2810 (6) |
Ba1—O3ix | 3.0909 (6) | O3—Mg2xxv | 2.0556 (6) |
Ba1—O3x | 3.0909 (6) | O3—Ba1iii | 2.7952 (6) |
Ba1—O3xi | 3.0910 (6) | O3—Ba1x | 3.0909 (6) |
Ba1—O3xii | 3.0910 (6) | C4—O3xxvi | 1.2809 (6) |
Mg2—O3xiii | 2.0556 (6) | C4—O3xxvii | 1.2809 (6) |
Mg2—O3xiv | 2.0556 (6) | C4—O3xxviii | 1.2809 (6) |
Mg2—O3xv | 2.0556 (6) | C4—Ba1xxii | 3.2907 (4) |
Mg2—O3xvi | 2.0556 (6) | C4—Ba1xx | 3.2907 (4) |
Mg2—O3xvii | 2.0556 (6) | C4—Ba1iii | 3.2908 (4) |
O3i—Ba1—O3ii | 123.70 (2) | O3xiv—Mg2—O3xviii | 86.90 (2) |
O3i—Ba1—O3iii | 137.56 (2) | O3xv—Mg2—O3xviii | 93.10 (2) |
O3ii—Ba1—O3iii | 92.790 (17) | O3xvi—Mg2—O3xviii | 86.90 (2) |
O3i—Ba1—O3iv | 92.790 (17) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 137.56 (2) | O3xiii—Mg2—Ba1xix | 98.477 (17) |
O3iii—Ba1—O3iv | 67.03 (3) | O3xiv—Mg2—Ba1xix | 81.523 (17) |
O3i—Ba1—O3v | 92.790 (17) | O3xv—Mg2—Ba1xix | 40.651 (16) |
O3ii—Ba1—O3v | 67.03 (3) | O3xvi—Mg2—Ba1xix | 139.349 (16) |
O3iii—Ba1—O3v | 123.70 (2) | O3xvii—Mg2—Ba1xix | 49.219 (17) |
O3iv—Ba1—O3v | 92.789 (17) | O3xviii—Mg2—Ba1xix | 130.781 (17) |
O3i—Ba1—O3vi | 67.03 (3) | O3xiii—Mg2—Ba1xx | 81.523 (17) |
O3ii—Ba1—O3vi | 92.790 (17) | O3xiv—Mg2—Ba1xx | 98.477 (17) |
O3iii—Ba1—O3vi | 92.789 (17) | O3xv—Mg2—Ba1xx | 139.349 (16) |
O3iv—Ba1—O3vi | 123.70 (2) | O3xvi—Mg2—Ba1xx | 40.651 (16) |
O3v—Ba1—O3vi | 137.56 (2) | O3xvii—Mg2—Ba1xx | 130.781 (17) |
O3i—Ba1—O3vii | 176.440 (13) | O3xviii—Mg2—Ba1xx | 49.219 (17) |
O3ii—Ba1—O3vii | 57.15 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.91 (2) | O3xiii—Mg2—Ba1xxi | 49.218 (17) |
O3iv—Ba1—O3vii | 85.140 (13) | O3xiv—Mg2—Ba1xxi | 130.782 (17) |
O3v—Ba1—O3vii | 84.430 (13) | O3xv—Mg2—Ba1xxi | 98.477 (17) |
O3vi—Ba1—O3vii | 116.53 (2) | O3xvi—Mg2—Ba1xxi | 81.523 (17) |
O3i—Ba1—O3viii | 57.15 (2) | O3xvii—Mg2—Ba1xxi | 40.653 (16) |
O3ii—Ba1—O3viii | 176.440 (13) | O3xviii—Mg2—Ba1xxi | 139.347 (16) |
O3iii—Ba1—O3viii | 85.140 (13) | Ba1xix—Mg2—Ba1xxi | 77.216 (2) |
O3iv—Ba1—O3viii | 43.91 (2) | Ba1xx—Mg2—Ba1xxi | 102.784 (2) |
O3v—Ba1—O3viii | 116.53 (2) | O3xiii—Mg2—Ba1xxii | 130.782 (17) |
O3vi—Ba1—O3viii | 84.430 (13) | O3xiv—Mg2—Ba1xxii | 49.218 (17) |
O3vii—Ba1—O3viii | 122.25 (2) | O3xv—Mg2—Ba1xxii | 81.523 (17) |
O3i—Ba1—O3ix | 43.91 (2) | O3xvi—Mg2—Ba1xxii | 98.477 (17) |
O3ii—Ba1—O3ix | 84.430 (13) | O3xvii—Mg2—Ba1xxii | 139.347 (16) |
O3iii—Ba1—O3ix | 176.440 (13) | O3xviii—Mg2—Ba1xxii | 40.653 (16) |
O3iv—Ba1—O3ix | 116.53 (2) | Ba1xix—Mg2—Ba1xxii | 102.784 (2) |
O3v—Ba1—O3ix | 57.15 (2) | Ba1xx—Mg2—Ba1xxii | 77.216 (2) |
O3vi—Ba1—O3ix | 85.141 (14) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 134.89 (2) | O3xiii—Mg2—Ba1xxiii | 40.653 (16) |
O3viii—Ba1—O3ix | 97.522 (14) | O3xiv—Mg2—Ba1xxiii | 139.347 (17) |
O3i—Ba1—O3x | 84.430 (13) | O3xv—Mg2—Ba1xxiii | 49.219 (17) |
O3ii—Ba1—O3x | 43.91 (2) | O3xvi—Mg2—Ba1xxiii | 130.781 (17) |
O3iii—Ba1—O3x | 116.53 (2) | O3xvii—Mg2—Ba1xxiii | 98.478 (17) |
O3iv—Ba1—O3x | 176.440 (13) | O3xviii—Mg2—Ba1xxiii | 81.522 (17) |
O3v—Ba1—O3x | 85.141 (14) | Ba1xix—Mg2—Ba1xxiii | 77.215 (3) |
O3vi—Ba1—O3x | 57.15 (2) | Ba1xx—Mg2—Ba1xxiii | 102.785 (3) |
O3vii—Ba1—O3x | 97.522 (14) | Ba1xxi—Mg2—Ba1xxiii | 77.215 (2) |
O3viii—Ba1—O3x | 134.89 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.785 (2) |
O3ix—Ba1—O3x | 59.91 (2) | O3xiii—Mg2—Ba1iii | 139.347 (17) |
O3i—Ba1—O3xi | 85.141 (14) | O3xiv—Mg2—Ba1iii | 40.653 (16) |
O3ii—Ba1—O3xi | 116.53 (2) | O3xv—Mg2—Ba1iii | 130.781 (17) |
O3iii—Ba1—O3xi | 57.15 (2) | O3xvi—Mg2—Ba1iii | 49.219 (17) |
O3iv—Ba1—O3xi | 84.430 (13) | O3xvii—Mg2—Ba1iii | 81.522 (17) |
O3v—Ba1—O3xi | 176.440 (13) | O3xviii—Mg2—Ba1iii | 98.478 (17) |
O3vi—Ba1—O3xi | 43.91 (2) | Ba1xix—Mg2—Ba1iii | 102.785 (3) |
O3vii—Ba1—O3xi | 97.522 (14) | Ba1xx—Mg2—Ba1iii | 77.215 (3) |
O3viii—Ba1—O3xi | 59.91 (2) | Ba1xxi—Mg2—Ba1iii | 102.785 (2) |
O3ix—Ba1—O3xi | 122.25 (2) | Ba1xxii—Mg2—Ba1iii | 77.215 (2) |
O3x—Ba1—O3xi | 97.522 (14) | Ba1xxiii—Mg2—Ba1iii | 180.0 |
O3i—Ba1—O3xii | 116.53 (2) | C4xxiv—O3—Mg2xxv | 138.81 (5) |
O3ii—Ba1—O3xii | 85.141 (14) | C4xxiv—O3—Ba1iii | 101.07 (4) |
O3iii—Ba1—O3xii | 84.430 (13) | Mg2xxv—O3—Ba1iii | 110.72 (2) |
O3iv—Ba1—O3xii | 57.15 (2) | C4xxiv—O3—Ba1x | 87.35 (3) |
O3v—Ba1—O3xii | 43.91 (2) | Mg2xxv—O3—Ba1x | 100.54 (2) |
O3vi—Ba1—O3xii | 176.440 (13) | Ba1iii—O3—Ba1x | 116.53 (2) |
O3vii—Ba1—O3xii | 59.91 (2) | O3xxvi—C4—O3xxvii | 119.914 (5) |
O3viii—Ba1—O3xii | 97.522 (14) | O3xxvi—C4—O3xxviii | 119.914 (5) |
O3ix—Ba1—O3xii | 97.522 (14) | O3xxvii—C4—O3xxviii | 119.914 (5) |
O3x—Ba1—O3xii | 122.25 (2) | O3xxvi—C4—Ba1xxii | 148.89 (6) |
O3xi—Ba1—O3xii | 134.89 (2) | O3xxvii—C4—Ba1xxii | 69.76 (3) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxviii—C4—Ba1xxii | 56.47 (3) |
O3xiii—Mg2—O3xv | 86.90 (2) | O3xxvi—C4—Ba1xx | 56.47 (3) |
O3xiv—Mg2—O3xv | 93.10 (2) | O3xxvii—C4—Ba1xx | 148.89 (6) |
O3xiii—Mg2—O3xvi | 93.10 (2) | O3xxviii—C4—Ba1xx | 69.76 (3) |
O3xiv—Mg2—O3xvi | 86.90 (2) | Ba1xxii—C4—Ba1xx | 99.102 (17) |
O3xv—Mg2—O3xvi | 180.00 (4) | O3xxvi—C4—Ba1iii | 69.76 (3) |
O3xiii—Mg2—O3xvii | 86.90 (2) | O3xxvii—C4—Ba1iii | 56.47 (3) |
O3xiv—Mg2—O3xvii | 93.10 (2) | O3xxviii—C4—Ba1iii | 148.89 (6) |
O3xv—Mg2—O3xvii | 86.90 (2) | Ba1xxii—C4—Ba1iii | 99.101 (17) |
O3xvi—Mg2—O3xvii | 93.10 (2) | Ba1xx—C4—Ba1iii | 99.101 (17) |
O3xiii—Mg2—O3xviii | 93.10 (2) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.850 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9363 reflections |
a = 5.0113 (1) Å | θ = 1.5–45° |
c = 33.5158 (10) Å | µ = 8.26 mm−1 |
V = 728.92 (4) Å3 | T = 200 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.030 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9363 measured reflections | k = −9→10 |
697 independent reflections | l = −34→65 |
515 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0117P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.020 | (Δ/σ)max < 0.001 |
S = 0.95 | Δρmax = 0.54 e Å−3 |
697 reflections | Δρmin = −0.58 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.00759 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00639 (7) | |
O3 | 0.11331 (15) | 0.82114 (14) | 0.12927 (2) | 0.01391 (11) | |
C4 | 0.0000 | 0.0000 | 0.13034 (3) | 0.00705 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00656 (2) | 0.00656 (2) | 0.00965 (3) | 0.00328 (1) | 0.000 | 0.000 |
Mg2 | 0.00542 (10) | 0.00542 (10) | 0.00834 (16) | 0.00271 (5) | 0.000 | 0.000 |
O3 | 0.0180 (3) | 0.0150 (3) | 0.01585 (18) | 0.0135 (3) | −0.00596 (18) | −0.00361 (18) |
C4 | 0.00680 (16) | 0.00680 (16) | 0.0076 (2) | 0.00340 (8) | 0.000 | 0.000 |
Ba1—O3i | 2.8079 (6) | Mg2—O3xviii | 2.0589 (6) |
Ba1—O3ii | 2.8079 (6) | Mg2—Ba1xix | 4.0215 (1) |
Ba1—O3iii | 2.8079 (6) | Mg2—Ba1xx | 4.0215 (1) |
Ba1—O3iv | 2.8079 (6) | Mg2—Ba1xxi | 4.0215 (1) |
Ba1—O3v | 2.8079 (6) | Mg2—Ba1xxii | 4.0215 (1) |
Ba1—O3vi | 2.8079 (6) | Mg2—Ba1xxiii | 4.0215 (1) |
Ba1—O3vii | 3.0872 (7) | Mg2—Ba1i | 4.0215 (1) |
Ba1—O3viii | 3.0872 (6) | O3—C4xxiv | 1.2791 (6) |
Ba1—O3ix | 3.0872 (6) | O3—Mg2xxv | 2.0589 (6) |
Ba1—O3x | 3.0872 (7) | O3—Ba1i | 2.8079 (6) |
Ba1—O3xi | 3.0872 (6) | O3—Ba1x | 3.0872 (6) |
Ba1—O3xii | 3.0872 (6) | C4—O3xxvi | 1.2791 (6) |
Mg2—O3xiii | 2.0589 (6) | C4—O3xxvii | 1.2791 (6) |
Mg2—O3xiv | 2.0589 (6) | C4—O3xxviii | 1.2791 (6) |
Mg2—O3xv | 2.0589 (6) | C4—Ba1xxii | 3.2943 (4) |
Mg2—O3xvi | 2.0589 (6) | C4—Ba1xx | 3.2943 (4) |
Mg2—O3xvii | 2.0589 (6) | C4—Ba1i | 3.2944 (4) |
O3i—Ba1—O3ii | 137.57 (2) | O3xiv—Mg2—O3xviii | 86.80 (2) |
O3i—Ba1—O3iii | 123.67 (2) | O3xv—Mg2—O3xviii | 93.20 (2) |
O3ii—Ba1—O3iii | 92.811 (18) | O3xvi—Mg2—O3xviii | 86.80 (2) |
O3i—Ba1—O3iv | 67.01 (3) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 92.811 (18) | O3xiii—Mg2—Ba1xix | 98.346 (17) |
O3iii—Ba1—O3iv | 92.811 (18) | O3xiv—Mg2—Ba1xix | 81.654 (17) |
O3i—Ba1—O3v | 92.811 (18) | O3xv—Mg2—Ba1xix | 40.848 (17) |
O3ii—Ba1—O3v | 67.01 (3) | O3xvi—Mg2—Ba1xix | 139.152 (17) |
O3iii—Ba1—O3v | 137.57 (3) | O3xvii—Mg2—Ba1xix | 48.928 (18) |
O3iv—Ba1—O3v | 123.67 (2) | O3xviii—Mg2—Ba1xix | 131.072 (18) |
O3i—Ba1—O3vi | 92.811 (18) | O3xiii—Mg2—Ba1xx | 81.654 (17) |
O3ii—Ba1—O3vi | 123.67 (2) | O3xiv—Mg2—Ba1xx | 98.346 (17) |
O3iii—Ba1—O3vi | 67.01 (3) | O3xv—Mg2—Ba1xx | 139.152 (17) |
O3iv—Ba1—O3vi | 137.57 (2) | O3xvi—Mg2—Ba1xx | 40.848 (17) |
O3v—Ba1—O3vi | 92.811 (18) | O3xvii—Mg2—Ba1xx | 131.072 (18) |
O3i—Ba1—O3vii | 176.633 (14) | O3xviii—Mg2—Ba1xx | 48.928 (18) |
O3ii—Ba1—O3vii | 43.81 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 57.13 (2) | O3xiii—Mg2—Ba1xxi | 48.926 (18) |
O3iv—Ba1—O3vii | 116.36 (2) | O3xiv—Mg2—Ba1xxi | 131.074 (18) |
O3v—Ba1—O3vii | 85.233 (14) | O3xv—Mg2—Ba1xxi | 98.346 (17) |
O3vi—Ba1—O3vii | 84.558 (13) | O3xvi—Mg2—Ba1xxi | 81.654 (17) |
O3i—Ba1—O3viii | 43.81 (2) | O3xvii—Mg2—Ba1xxi | 40.850 (17) |
O3ii—Ba1—O3viii | 176.633 (13) | O3xviii—Mg2—Ba1xxi | 139.150 (17) |
O3iii—Ba1—O3viii | 84.558 (13) | Ba1xix—Mg2—Ba1xxi | 77.081 (2) |
O3iv—Ba1—O3viii | 85.233 (14) | Ba1xx—Mg2—Ba1xxi | 102.919 (2) |
O3v—Ba1—O3viii | 116.36 (2) | O3xiii—Mg2—Ba1xxii | 131.074 (18) |
O3vi—Ba1—O3viii | 57.13 (2) | O3xiv—Mg2—Ba1xxii | 48.926 (18) |
O3vii—Ba1—O3viii | 135.05 (2) | O3xv—Mg2—Ba1xxii | 81.654 (17) |
O3i—Ba1—O3ix | 57.13 (2) | O3xvi—Mg2—Ba1xxii | 98.346 (17) |
O3ii—Ba1—O3ix | 85.233 (14) | O3xvii—Mg2—Ba1xxii | 139.150 (17) |
O3iii—Ba1—O3ix | 176.633 (13) | O3xviii—Mg2—Ba1xxii | 40.850 (17) |
O3iv—Ba1—O3ix | 84.558 (13) | Ba1xix—Mg2—Ba1xxii | 102.919 (2) |
O3v—Ba1—O3ix | 43.81 (2) | Ba1xx—Mg2—Ba1xxii | 77.081 (2) |
O3vi—Ba1—O3ix | 116.36 (2) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 122.30 (2) | O3xiii—Mg2—Ba1xxiii | 40.850 (17) |
O3viii—Ba1—O3ix | 97.293 (14) | O3xiv—Mg2—Ba1xxiii | 139.150 (17) |
O3i—Ba1—O3x | 116.36 (2) | O3xv—Mg2—Ba1xxiii | 48.928 (18) |
O3ii—Ba1—O3x | 84.558 (13) | O3xvi—Mg2—Ba1xxiii | 131.072 (18) |
O3iii—Ba1—O3x | 85.233 (14) | O3xvii—Mg2—Ba1xxiii | 98.348 (17) |
O3iv—Ba1—O3x | 176.633 (14) | O3xviii—Mg2—Ba1xxiii | 81.652 (17) |
O3v—Ba1—O3x | 57.13 (2) | Ba1xix—Mg2—Ba1xxiii | 77.081 (1) |
O3vi—Ba1—O3x | 43.81 (2) | Ba1xx—Mg2—Ba1xxiii | 102.919 (1) |
O3vii—Ba1—O3x | 60.27 (2) | Ba1xxi—Mg2—Ba1xxiii | 77.081 (2) |
O3viii—Ba1—O3x | 97.293 (14) | Ba1xxii—Mg2—Ba1xxiii | 102.919 (2) |
O3ix—Ba1—O3x | 97.293 (14) | O3xiii—Mg2—Ba1i | 139.150 (17) |
O3i—Ba1—O3xi | 85.233 (14) | O3xiv—Mg2—Ba1i | 40.850 (17) |
O3ii—Ba1—O3xi | 57.13 (2) | O3xv—Mg2—Ba1i | 131.072 (18) |
O3iii—Ba1—O3xi | 116.36 (2) | O3xvi—Mg2—Ba1i | 48.928 (18) |
O3iv—Ba1—O3xi | 43.81 (2) | O3xvii—Mg2—Ba1i | 81.652 (17) |
O3v—Ba1—O3xi | 84.558 (13) | O3xviii—Mg2—Ba1i | 98.348 (17) |
O3vi—Ba1—O3xi | 176.633 (13) | Ba1xix—Mg2—Ba1i | 102.919 (1) |
O3vii—Ba1—O3xi | 97.293 (14) | Ba1xx—Mg2—Ba1i | 77.081 (1) |
O3viii—Ba1—O3xi | 122.30 (2) | Ba1xxi—Mg2—Ba1i | 102.919 (2) |
O3ix—Ba1—O3xi | 60.27 (2) | Ba1xxii—Mg2—Ba1i | 77.081 (2) |
O3x—Ba1—O3xi | 135.05 (2) | Ba1xxiii—Mg2—Ba1i | 180.0 |
O3i—Ba1—O3xii | 84.558 (13) | C4xxiv—O3—Mg2xxv | 139.05 (6) |
O3ii—Ba1—O3xii | 116.36 (2) | C4xxiv—O3—Ba1i | 100.69 (4) |
O3iii—Ba1—O3xii | 43.81 (2) | Mg2xxv—O3—Ba1i | 110.49 (2) |
O3iv—Ba1—O3xii | 57.13 (2) | C4xxiv—O3—Ba1x | 87.72 (4) |
O3v—Ba1—O3xii | 176.633 (13) | Mg2xxv—O3—Ba1x | 100.89 (2) |
O3vi—Ba1—O3xii | 85.233 (14) | Ba1i—O3—Ba1x | 116.36 (2) |
O3vii—Ba1—O3xii | 97.293 (14) | O3xxvi—C4—O3xxvii | 119.923 (5) |
O3viii—Ba1—O3xii | 60.27 (2) | O3xxvi—C4—O3xxviii | 119.923 (5) |
O3ix—Ba1—O3xii | 135.05 (2) | O3xxvii—C4—O3xxviii | 119.921 (5) |
O3x—Ba1—O3xii | 122.30 (2) | O3xxvi—C4—Ba1xxii | 56.88 (3) |
O3xi—Ba1—O3xii | 97.293 (14) | O3xxvii—C4—Ba1xxii | 149.01 (6) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxviii—C4—Ba1xxii | 69.45 (3) |
O3xiii—Mg2—O3xv | 86.80 (2) | O3xxvi—C4—Ba1xx | 69.45 (3) |
O3xiv—Mg2—O3xv | 93.20 (2) | O3xxvii—C4—Ba1xx | 56.88 (3) |
O3xiii—Mg2—O3xvi | 93.20 (2) | O3xxviii—C4—Ba1xx | 149.01 (6) |
O3xiv—Mg2—O3xvi | 86.80 (2) | Ba1xxii—C4—Ba1xx | 99.033 (17) |
O3xv—Mg2—O3xvi | 180.00 (5) | O3xxvi—C4—Ba1i | 149.01 (6) |
O3xiii—Mg2—O3xvii | 86.80 (2) | O3xxvii—C4—Ba1i | 69.45 (3) |
O3xiv—Mg2—O3xvii | 93.20 (2) | O3xxviii—C4—Ba1i | 56.88 (3) |
O3xv—Mg2—O3xvii | 86.80 (2) | Ba1xxii—C4—Ba1i | 99.032 (17) |
O3xvi—Mg2—O3xvii | 93.20 (2) | Ba1xx—C4—Ba1i | 99.032 (17) |
O3xiii—Mg2—O3xviii | 93.20 (2) |
Symmetry codes: (i) −x−1/3, −y+1/3, −z+1/3; (ii) −x+y−2/3, y−1/3, z+1/6; (iii) x+1/3, x−y+2/3, z+1/6; (iv) −y+1/3, −x−1/3, z+1/6; (v) x−y+2/3, x+1/3, −z+1/3; (vi) y−1/3, −x+y−2/3, −z+1/3; (vii) −y+4/3, −x+2/3, z+1/6; (viii) x−y+2/3, x−2/3, −z+1/3; (ix) y−4/3, −x+y−2/3, −z+1/3; (x) −x+2/3, −y+4/3, −z+1/3; (xi) x−2/3, x−y+2/3, z+1/6; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) x, y−1, z; (xxvii) −y+1, x−y+1, z; (xxviii) −x+y−1, −x, z. |
C6Ba3Mg3O18 | Dx = 3.851 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9496 reflections |
a = 5.0135 (1) Å | θ = 1.5–45° |
c = 33.4784 (9) Å | µ = 8.26 mm−1 |
V = 728.75 (4) Å3 | T = 250 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.031 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9496 measured reflections | k = −9→10 |
697 independent reflections | l = −34→65 |
488 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0112P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.021 | (Δ/σ)max < 0.001 |
S = 0.95 | Δρmax = 0.43 e Å−3 |
697 reflections | Δρmin = −0.60 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.00913 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00736 (7) | |
O3 | 0.11588 (17) | 0.82345 (17) | 0.12923 (2) | 0.01653 (13) | |
C4 | 0.0000 | 0.0000 | 0.13039 (3) | 0.00794 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00793 (2) | 0.00793 (2) | 0.01153 (3) | 0.00396 (1) | 0.000 | 0.000 |
Mg2 | 0.00632 (10) | 0.00632 (10) | 0.00942 (17) | 0.00316 (5) | 0.000 | 0.000 |
O3 | 0.0219 (4) | 0.0177 (3) | 0.0185 (2) | 0.0163 (3) | −0.0070 (2) | −0.0041 (2) |
C4 | 0.00766 (17) | 0.00766 (17) | 0.0085 (3) | 0.00383 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8171 (7) | Mg2—O3xviii | 2.0578 (6) |
Ba1—O3ii | 2.8171 (7) | Mg2—Ba1xix | 4.0202 (1) |
Ba1—O3iii | 2.8172 (7) | Mg2—Ba1xx | 4.0202 (1) |
Ba1—O3iv | 2.8172 (7) | Mg2—Ba1xxi | 4.0202 (1) |
Ba1—O3v | 2.8172 (7) | Mg2—Ba1xxii | 4.0202 (1) |
Ba1—O3vi | 2.8172 (7) | Mg2—Ba1xxiii | 4.0202 (1) |
Ba1—O3vii | 3.0759 (8) | Mg2—Ba1iii | 4.0202 (1) |
Ba1—O3viii | 3.0759 (8) | O3—C4xxiv | 1.2793 (6) |
Ba1—O3ix | 3.0759 (8) | O3—Mg2xxv | 2.0578 (6) |
Ba1—O3x | 3.0759 (8) | O3—Ba1iii | 2.8172 (7) |
Ba1—O3xi | 3.0759 (8) | O3—Ba1x | 3.0759 (8) |
Ba1—O3xii | 3.0759 (8) | C4—O3xxvi | 1.2793 (6) |
Mg2—O3xiii | 2.0577 (6) | C4—O3xxvii | 1.2793 (6) |
Mg2—O3xiv | 2.0577 (6) | C4—O3xxviii | 1.2793 (6) |
Mg2—O3xv | 2.0577 (6) | C4—Ba1xxii | 3.2955 (4) |
Mg2—O3xvi | 2.0577 (6) | C4—Ba1xx | 3.2955 (4) |
Mg2—O3xvii | 2.0578 (6) | C4—Ba1iii | 3.2955 (4) |
O3i—Ba1—O3ii | 123.60 (2) | O3xiv—Mg2—O3xviii | 86.76 (3) |
O3i—Ba1—O3iii | 137.39 (3) | O3xv—Mg2—O3xviii | 93.24 (3) |
O3ii—Ba1—O3iii | 93.09 (2) | O3xvi—Mg2—O3xviii | 86.76 (3) |
O3i—Ba1—O3iv | 93.09 (2) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 137.39 (3) | O3xiii—Mg2—Ba1xix | 98.387 (18) |
O3iii—Ba1—O3iv | 66.60 (3) | O3xiv—Mg2—Ba1xix | 81.613 (18) |
O3i—Ba1—O3v | 93.09 (2) | O3xv—Mg2—Ba1xix | 41.14 (2) |
O3ii—Ba1—O3v | 66.60 (3) | O3xvi—Mg2—Ba1xix | 138.86 (2) |
O3iii—Ba1—O3v | 123.60 (2) | O3xvii—Mg2—Ba1xix | 48.63 (2) |
O3iv—Ba1—O3v | 93.09 (2) | O3xviii—Mg2—Ba1xix | 131.37 (2) |
O3i—Ba1—O3vi | 66.60 (3) | O3xiii—Mg2—Ba1xx | 81.613 (18) |
O3ii—Ba1—O3vi | 93.09 (2) | O3xiv—Mg2—Ba1xx | 98.387 (18) |
O3iii—Ba1—O3vi | 93.09 (2) | O3xv—Mg2—Ba1xx | 138.86 (2) |
O3iv—Ba1—O3vi | 123.60 (2) | O3xvi—Mg2—Ba1xx | 41.14 (2) |
O3v—Ba1—O3vi | 137.39 (3) | O3xvii—Mg2—Ba1xx | 131.37 (2) |
O3i—Ba1—O3vii | 176.888 (16) | O3xviii—Mg2—Ba1xx | 48.63 (2) |
O3ii—Ba1—O3vii | 57.13 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.88 (2) | O3xiii—Mg2—Ba1xxi | 48.63 (2) |
O3iv—Ba1—O3vii | 85.108 (15) | O3xiv—Mg2—Ba1xxi | 131.37 (2) |
O3v—Ba1—O3vii | 84.487 (14) | O3xv—Mg2—Ba1xxi | 98.387 (18) |
O3vi—Ba1—O3vii | 116.52 (2) | O3xvi—Mg2—Ba1xxi | 81.613 (18) |
O3i—Ba1—O3viii | 57.13 (2) | O3xvii—Mg2—Ba1xxi | 41.15 (2) |
O3ii—Ba1—O3viii | 176.888 (16) | O3xviii—Mg2—Ba1xxi | 138.85 (2) |
O3iii—Ba1—O3viii | 85.108 (15) | Ba1xix—Mg2—Ba1xxi | 77.150 (1) |
O3iv—Ba1—O3viii | 43.88 (2) | Ba1xx—Mg2—Ba1xxi | 102.850 (2) |
O3v—Ba1—O3viii | 116.52 (2) | O3xiii—Mg2—Ba1xxii | 131.37 (2) |
O3vi—Ba1—O3viii | 84.487 (14) | O3xiv—Mg2—Ba1xxii | 48.63 (2) |
O3vii—Ba1—O3viii | 122.34 (2) | O3xv—Mg2—Ba1xxii | 81.613 (18) |
O3i—Ba1—O3ix | 43.88 (2) | O3xvi—Mg2—Ba1xxii | 98.387 (18) |
O3ii—Ba1—O3ix | 84.486 (14) | O3xvii—Mg2—Ba1xxii | 138.85 (2) |
O3iii—Ba1—O3ix | 176.888 (17) | O3xviii—Mg2—Ba1xxii | 41.15 (2) |
O3iv—Ba1—O3ix | 116.52 (2) | Ba1xix—Mg2—Ba1xxii | 102.850 (2) |
O3v—Ba1—O3ix | 57.12 (2) | Ba1xx—Mg2—Ba1xxii | 77.150 (1) |
O3vi—Ba1—O3ix | 85.108 (15) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.06 (2) | O3xiii—Mg2—Ba1xxiii | 41.15 (2) |
O3viii—Ba1—O3ix | 97.226 (16) | O3xiv—Mg2—Ba1xxiii | 138.85 (2) |
O3i—Ba1—O3x | 84.486 (14) | O3xv—Mg2—Ba1xxiii | 48.63 (2) |
O3ii—Ba1—O3x | 43.88 (2) | O3xvi—Mg2—Ba1xxiii | 131.37 (2) |
O3iii—Ba1—O3x | 116.52 (2) | O3xvii—Mg2—Ba1xxiii | 98.387 (18) |
O3iv—Ba1—O3x | 176.888 (17) | O3xviii—Mg2—Ba1xxiii | 81.613 (18) |
O3v—Ba1—O3x | 85.108 (15) | Ba1xix—Mg2—Ba1xxiii | 77.149 (1) |
O3vi—Ba1—O3x | 57.12 (2) | Ba1xx—Mg2—Ba1xxiii | 102.851 (1) |
O3vii—Ba1—O3x | 97.226 (16) | Ba1xxi—Mg2—Ba1xxiii | 77.149 (1) |
O3viii—Ba1—O3x | 135.06 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.851 (2) |
O3ix—Ba1—O3x | 60.37 (3) | O3xiii—Mg2—Ba1iii | 138.85 (2) |
O3i—Ba1—O3xi | 85.108 (15) | O3xiv—Mg2—Ba1iii | 41.15 (2) |
O3ii—Ba1—O3xi | 116.52 (2) | O3xv—Mg2—Ba1iii | 131.37 (2) |
O3iii—Ba1—O3xi | 57.12 (2) | O3xvi—Mg2—Ba1iii | 48.63 (2) |
O3iv—Ba1—O3xi | 84.487 (14) | O3xvii—Mg2—Ba1iii | 81.613 (18) |
O3v—Ba1—O3xi | 176.888 (16) | O3xviii—Mg2—Ba1iii | 98.387 (18) |
O3vi—Ba1—O3xi | 43.88 (2) | Ba1xix—Mg2—Ba1iii | 102.851 (1) |
O3vii—Ba1—O3xi | 97.226 (16) | Ba1xx—Mg2—Ba1iii | 77.149 (1) |
O3viii—Ba1—O3xi | 60.37 (2) | Ba1xxi—Mg2—Ba1iii | 102.851 (2) |
O3ix—Ba1—O3xi | 122.34 (2) | Ba1xxii—Mg2—Ba1iii | 77.149 (1) |
O3x—Ba1—O3xi | 97.226 (16) | Ba1xxiii—Mg2—Ba1iii | 180.0 |
O3i—Ba1—O3xii | 116.52 (2) | C4xxiv—O3—Mg2xxv | 139.14 (6) |
O3ii—Ba1—O3xii | 85.108 (15) | C4xxiv—O3—Ba1iii | 100.29 (4) |
O3iii—Ba1—O3xii | 84.487 (14) | Mg2xxv—O3—Ba1iii | 110.13 (3) |
O3iv—Ba1—O3xii | 57.12 (2) | C4xxiv—O3—Ba1x | 88.27 (4) |
O3v—Ba1—O3xii | 43.88 (2) | Mg2xxv—O3—Ba1x | 101.23 (3) |
O3vi—Ba1—O3xii | 176.888 (16) | Ba1iii—O3—Ba1x | 116.52 (2) |
O3vii—Ba1—O3xii | 60.37 (2) | O3xxvi—C4—O3xxvii | 119.908 (6) |
O3viii—Ba1—O3xii | 97.226 (16) | O3xxvi—C4—O3xxviii | 119.908 (6) |
O3ix—Ba1—O3xii | 97.226 (16) | O3xxvii—C4—O3xxviii | 119.908 (5) |
O3x—Ba1—O3xii | 122.34 (2) | O3xxvi—C4—Ba1xxii | 149.00 (6) |
O3xi—Ba1—O3xii | 135.06 (2) | O3xxvii—C4—Ba1xxii | 68.90 (4) |
O3xiii—Mg2—O3xiv | 180.00 (3) | O3xxviii—C4—Ba1xxii | 57.26 (4) |
O3xiii—Mg2—O3xv | 86.76 (3) | O3xxvi—C4—Ba1xx | 57.26 (4) |
O3xiv—Mg2—O3xv | 93.24 (3) | O3xxvii—C4—Ba1xx | 149.00 (6) |
O3xiii—Mg2—O3xvi | 93.24 (3) | O3xxviii—C4—Ba1xx | 68.90 (4) |
O3xiv—Mg2—O3xvi | 86.76 (3) | Ba1xxii—C4—Ba1xx | 99.046 (17) |
O3xv—Mg2—O3xvi | 180.00 (4) | O3xxvi—C4—Ba1iii | 68.90 (4) |
O3xiii—Mg2—O3xvii | 86.76 (3) | O3xxvii—C4—Ba1iii | 57.26 (4) |
O3xiv—Mg2—O3xvii | 93.24 (3) | O3xxviii—C4—Ba1iii | 149.00 (6) |
O3xv—Mg2—O3xvii | 86.76 (3) | Ba1xxii—C4—Ba1iii | 99.045 (17) |
O3xvi—Mg2—O3xvii | 93.24 (3) | Ba1xx—C4—Ba1iii | 99.045 (17) |
O3xiii—Mg2—O3xviii | 93.24 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.845 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9450 reflections |
a = 5.0161 (1) Å | θ = 1.5–40° |
c = 33.4952 (8) Å | µ = 8.25 mm−1 |
V = 729.87 (3) Å3 | T = 280 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9450 measured reflections | k = −9→10 |
699 independent reflections | l = −36→66 |
507 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0127P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.023 | (Δ/σ)max < 0.001 |
S = 1.03 | Δρmax = 0.53 e Å−3 |
699 reflections | Δρmin = −0.40 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.00992 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00804 (7) | |
O3 | 0.11770 (16) | 0.82531 (16) | 0.12921 (2) | 0.01808 (12) | |
C4 | 0.0000 | 0.0000 | 0.13039 (3) | 0.00870 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00867 (2) | 0.00867 (2) | 0.01241 (3) | 0.00434 (1) | 0.000 | 0.000 |
Mg2 | 0.00690 (11) | 0.00690 (11) | 0.01031 (17) | 0.00345 (5) | 0.000 | 0.000 |
O3 | 0.0236 (3) | 0.0198 (3) | 0.0202 (2) | 0.0179 (3) | −0.0075 (2) | −0.0043 (2) |
C4 | 0.00849 (17) | 0.00849 (17) | 0.0091 (3) | 0.00424 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8261 (7) | Mg2—O3xviii | 2.0586 (6) |
Ba1—O3ii | 2.8261 (7) | Mg2—Ba1xix | 4.0223 (1) |
Ba1—O3iii | 2.8261 (7) | Mg2—Ba1xx | 4.0223 (1) |
Ba1—O3iv | 2.8261 (7) | Mg2—Ba1xxi | 4.0223 (1) |
Ba1—O3v | 2.8261 (7) | Mg2—Ba1xxii | 4.0223 (1) |
Ba1—O3vi | 2.8261 (7) | Mg2—Ba1xxiii | 4.0223 (1) |
Ba1—O3vii | 3.0693 (7) | Mg2—Ba1iii | 4.0223 (1) |
Ba1—O3viii | 3.0693 (7) | O3—C4xxiv | 1.2788 (6) |
Ba1—O3ix | 3.0693 (8) | O3—Mg2xxv | 2.0585 (6) |
Ba1—O3x | 3.0693 (8) | O3—Ba1iii | 2.8261 (7) |
Ba1—O3xi | 3.0693 (7) | O3—Ba1x | 3.0693 (7) |
Ba1—O3xii | 3.0693 (7) | C4—O3xxvi | 1.2788 (6) |
Mg2—O3xiii | 2.0586 (6) | C4—O3xxvii | 1.2788 (6) |
Mg2—O3xiv | 2.0586 (6) | C4—O3xxviii | 1.2788 (6) |
Mg2—O3xv | 2.0586 (6) | C4—Ba1xxii | 3.2971 (4) |
Mg2—O3xvi | 2.0586 (6) | C4—Ba1xx | 3.2971 (4) |
Mg2—O3xvii | 2.0586 (6) | C4—Ba1iii | 3.2971 (4) |
O3i—Ba1—O3ii | 123.55 (3) | O3xiv—Mg2—O3xviii | 86.73 (3) |
O3i—Ba1—O3iii | 137.32 (3) | O3xv—Mg2—O3xviii | 93.27 (3) |
O3ii—Ba1—O3iii | 93.24 (2) | O3xvi—Mg2—O3xviii | 86.73 (3) |
O3i—Ba1—O3iv | 93.24 (2) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 137.32 (3) | O3xiii—Mg2—Ba1xix | 98.382 (19) |
O3iii—Ba1—O3iv | 66.37 (3) | O3xiv—Mg2—Ba1xix | 81.618 (19) |
O3i—Ba1—O3v | 93.24 (2) | O3xv—Mg2—Ba1xix | 41.363 (19) |
O3ii—Ba1—O3v | 66.37 (3) | O3xvi—Mg2—Ba1xix | 138.637 (19) |
O3iii—Ba1—O3v | 123.55 (2) | O3xvii—Mg2—Ba1xix | 48.40 (2) |
O3iv—Ba1—O3v | 93.24 (2) | O3xviii—Mg2—Ba1xix | 131.60 (2) |
O3i—Ba1—O3vi | 66.37 (3) | O3xiii—Mg2—Ba1xx | 81.618 (19) |
O3ii—Ba1—O3vi | 93.24 (2) | O3xiv—Mg2—Ba1xx | 98.382 (19) |
O3iii—Ba1—O3vi | 93.24 (2) | O3xv—Mg2—Ba1xx | 138.637 (19) |
O3iv—Ba1—O3vi | 123.55 (2) | O3xvi—Mg2—Ba1xx | 41.363 (19) |
O3v—Ba1—O3vi | 137.32 (3) | O3xvii—Mg2—Ba1xx | 131.60 (2) |
O3i—Ba1—O3vii | 177.078 (15) | O3xviii—Mg2—Ba1xx | 48.40 (2) |
O3ii—Ba1—O3vii | 57.13 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.87 (2) | O3xiii—Mg2—Ba1xxi | 48.40 (2) |
O3iv—Ba1—O3vii | 85.069 (15) | O3xiv—Mg2—Ba1xxi | 131.60 (2) |
O3v—Ba1—O3vii | 84.485 (15) | O3xv—Mg2—Ba1xxi | 98.382 (19) |
O3vi—Ba1—O3vii | 116.55 (2) | O3xvi—Mg2—Ba1xxi | 81.618 (19) |
O3i—Ba1—O3viii | 57.13 (2) | O3xvii—Mg2—Ba1xxi | 41.364 (19) |
O3ii—Ba1—O3viii | 177.078 (15) | O3xviii—Mg2—Ba1xxi | 138.636 (19) |
O3iii—Ba1—O3viii | 85.069 (15) | Ba1xix—Mg2—Ba1xxi | 77.150 (1) |
O3iv—Ba1—O3viii | 43.87 (2) | Ba1xx—Mg2—Ba1xxi | 102.850 (1) |
O3v—Ba1—O3viii | 116.55 (2) | O3xiii—Mg2—Ba1xxii | 131.60 (2) |
O3vi—Ba1—O3viii | 84.485 (15) | O3xiv—Mg2—Ba1xxii | 48.40 (2) |
O3vii—Ba1—O3viii | 122.36 (2) | O3xv—Mg2—Ba1xxii | 81.618 (19) |
O3i—Ba1—O3ix | 43.87 (2) | O3xvi—Mg2—Ba1xxii | 98.382 (19) |
O3ii—Ba1—O3ix | 84.485 (15) | O3xvii—Mg2—Ba1xxii | 138.636 (19) |
O3iii—Ba1—O3ix | 177.078 (16) | O3xviii—Mg2—Ba1xxii | 41.364 (19) |
O3iv—Ba1—O3ix | 116.55 (2) | Ba1xix—Mg2—Ba1xxii | 102.850 (1) |
O3v—Ba1—O3ix | 57.13 (2) | Ba1xx—Mg2—Ba1xxii | 77.150 (1) |
O3vi—Ba1—O3ix | 85.070 (15) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.13 (2) | O3xiii—Mg2—Ba1xxiii | 41.364 (19) |
O3viii—Ba1—O3ix | 97.125 (16) | O3xiv—Mg2—Ba1xxiii | 138.636 (19) |
O3i—Ba1—O3x | 84.485 (15) | O3xv—Mg2—Ba1xxiii | 48.40 (2) |
O3ii—Ba1—O3x | 43.87 (2) | O3xvi—Mg2—Ba1xxiii | 131.60 (2) |
O3iii—Ba1—O3x | 116.55 (2) | O3xvii—Mg2—Ba1xxiii | 98.383 (19) |
O3iv—Ba1—O3x | 177.078 (16) | O3xviii—Mg2—Ba1xxiii | 81.617 (19) |
O3v—Ba1—O3x | 85.070 (15) | Ba1xix—Mg2—Ba1xxiii | 77.150 (1) |
O3vi—Ba1—O3x | 57.13 (2) | Ba1xx—Mg2—Ba1xxiii | 102.850 (2) |
O3vii—Ba1—O3x | 97.125 (16) | Ba1xxi—Mg2—Ba1xxiii | 77.150 (1) |
O3viii—Ba1—O3x | 135.13 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.850 (1) |
O3ix—Ba1—O3x | 60.53 (3) | O3xiii—Mg2—Ba1iii | 138.636 (19) |
O3i—Ba1—O3xi | 85.070 (15) | O3xiv—Mg2—Ba1iii | 41.364 (19) |
O3ii—Ba1—O3xi | 116.55 (2) | O3xv—Mg2—Ba1iii | 131.60 (2) |
O3iii—Ba1—O3xi | 57.13 (2) | O3xvi—Mg2—Ba1iii | 48.40 (2) |
O3iv—Ba1—O3xi | 84.486 (15) | O3xvii—Mg2—Ba1iii | 81.617 (19) |
O3v—Ba1—O3xi | 177.078 (15) | O3xviii—Mg2—Ba1iii | 98.383 (19) |
O3vi—Ba1—O3xi | 43.87 (2) | Ba1xix—Mg2—Ba1iii | 102.850 (2) |
O3vii—Ba1—O3xi | 97.125 (16) | Ba1xx—Mg2—Ba1iii | 77.150 (1) |
O3viii—Ba1—O3xi | 60.53 (3) | Ba1xxi—Mg2—Ba1iii | 102.850 (1) |
O3ix—Ba1—O3xi | 122.36 (2) | Ba1xxii—Mg2—Ba1iii | 77.150 (1) |
O3x—Ba1—O3xi | 97.125 (16) | Ba1xxiii—Mg2—Ba1iii | 180.0 |
O3i—Ba1—O3xii | 116.55 (2) | C4xxiv—O3—Mg2xxv | 139.29 (6) |
O3ii—Ba1—O3xii | 85.070 (15) | C4xxiv—O3—Ba1iii | 99.95 (4) |
O3iii—Ba1—O3xii | 84.486 (15) | Mg2xxv—O3—Ba1iii | 109.86 (3) |
O3iv—Ba1—O3xii | 57.13 (2) | C4xxiv—O3—Ba1x | 88.65 (4) |
O3v—Ba1—O3xii | 43.87 (2) | Mg2xxv—O3—Ba1x | 101.50 (3) |
O3vi—Ba1—O3xii | 177.078 (15) | Ba1iii—O3—Ba1x | 116.55 (2) |
O3vii—Ba1—O3xii | 60.53 (3) | O3xxvi—C4—O3xxvii | 119.906 (6) |
O3viii—Ba1—O3xii | 97.125 (16) | O3xxvi—C4—O3xxviii | 119.906 (6) |
O3ix—Ba1—O3xii | 97.125 (16) | O3xxvii—C4—O3xxviii | 119.906 (6) |
O3x—Ba1—O3xii | 122.36 (2) | O3xxvi—C4—Ba1xxii | 149.06 (6) |
O3xi—Ba1—O3xii | 135.13 (2) | O3xxvii—C4—Ba1xxii | 68.54 (4) |
O3xiii—Mg2—O3xiv | 180.00 (7) | O3xxviii—C4—Ba1xxii | 57.59 (4) |
O3xiii—Mg2—O3xv | 86.73 (3) | O3xxvi—C4—Ba1xx | 57.59 (4) |
O3xiv—Mg2—O3xv | 93.27 (3) | O3xxvii—C4—Ba1xx | 149.06 (6) |
O3xiii—Mg2—O3xvi | 93.27 (3) | O3xxviii—C4—Ba1xx | 68.54 (4) |
O3xiv—Mg2—O3xvi | 86.73 (3) | Ba1xxii—C4—Ba1xx | 99.049 (18) |
O3xv—Mg2—O3xvi | 180.00 (5) | O3xxvi—C4—Ba1iii | 68.54 (4) |
O3xiii—Mg2—O3xvii | 86.73 (3) | O3xxvii—C4—Ba1iii | 57.59 (4) |
O3xiv—Mg2—O3xvii | 93.27 (3) | O3xxviii—C4—Ba1iii | 149.06 (6) |
O3xv—Mg2—O3xvii | 86.73 (3) | Ba1xxii—C4—Ba1iii | 99.048 (18) |
O3xvi—Mg2—O3xvii | 93.27 (3) | Ba1xx—C4—Ba1iii | 99.048 (18) |
O3xiii—Mg2—O3xviii | 93.27 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.843 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9325 reflections |
a = 5.0160 (1) Å | θ = 1.5–45° |
c = 33.5170 (13) Å | µ = 8.24 mm−1 |
V = 730.32 (4) Å3 | T = 299 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.031 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9325 measured reflections | k = −9→10 |
698 independent reflections | l = −35→66 |
490 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0135P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.023 | (Δ/σ)max < 0.001 |
S = 0.95 | Δρmax = 0.54 e Å−3 |
698 reflections | Δρmin = −0.52 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01061 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00849 (7) | |
O3 | 0.11931 (18) | 0.82676 (17) | 0.12918 (2) | 0.01925 (13) | |
C4 | 0.0000 | 0.0000 | 0.13035 (3) | 0.00915 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00913 (2) | 0.00913 (2) | 0.01358 (3) | 0.00456 (1) | 0.000 | 0.000 |
Mg2 | 0.00708 (11) | 0.00708 (11) | 0.01131 (17) | 0.00354 (5) | 0.000 | 0.000 |
O3 | 0.0253 (4) | 0.0211 (3) | 0.0214 (2) | 0.0192 (3) | −0.0077 (3) | −0.0044 (2) |
C4 | 0.00867 (17) | 0.00867 (17) | 0.0101 (3) | 0.00434 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8324 (7) | Mg2—O3xviii | 2.0586 (6) |
Ba1—O3ii | 2.8324 (7) | Mg2—Ba1xix | 4.0235 (1) |
Ba1—O3iii | 2.8324 (8) | Mg2—Ba1xx | 4.0235 (1) |
Ba1—O3iv | 2.8324 (8) | Mg2—Ba1xxi | 4.0235 (1) |
Ba1—O3v | 2.8324 (7) | Mg2—Ba1xxii | 4.0235 (1) |
Ba1—O3vi | 2.8324 (7) | Mg2—Ba1xxiii | 4.0235 (1) |
Ba1—O3vii | 3.0625 (8) | Mg2—Ba1iii | 4.0235 (1) |
Ba1—O3viii | 3.0625 (8) | O3—C4xxiv | 1.2786 (6) |
Ba1—O3ix | 3.0626 (8) | O3—Mg2xxv | 2.0586 (6) |
Ba1—O3x | 3.0626 (8) | O3—Ba1iii | 2.8323 (7) |
Ba1—O3xi | 3.0626 (8) | O3—Ba1x | 3.0625 (8) |
Ba1—O3xii | 3.0626 (8) | C4—O3xxvi | 1.2786 (6) |
Mg2—O3xiii | 2.0586 (6) | C4—O3xxvii | 1.2786 (6) |
Mg2—O3xiv | 2.0586 (6) | C4—O3xxviii | 1.2786 (6) |
Mg2—O3xv | 2.0586 (6) | C4—Ba1xxii | 3.2969 (4) |
Mg2—O3xvi | 2.0586 (6) | C4—Ba1xx | 3.2969 (4) |
Mg2—O3xvii | 2.0586 (6) | C4—Ba1iii | 3.2970 (4) |
O3i—Ba1—O3ii | 123.54 (3) | O3xiv—Mg2—O3xviii | 86.64 (3) |
O3i—Ba1—O3iii | 137.22 (3) | O3xv—Mg2—O3xviii | 93.36 (3) |
O3ii—Ba1—O3iii | 93.36 (2) | O3xvi—Mg2—O3xviii | 86.64 (3) |
O3i—Ba1—O3iv | 93.36 (2) | O3xvii—Mg2—O3xviii | 180.00 (4) |
O3ii—Ba1—O3iv | 137.22 (3) | O3xiii—Mg2—Ba1xix | 98.311 (19) |
O3iii—Ba1—O3iv | 66.20 (3) | O3xiv—Mg2—Ba1xix | 81.689 (19) |
O3i—Ba1—O3v | 93.36 (2) | O3xv—Mg2—Ba1xix | 41.52 (2) |
O3ii—Ba1—O3v | 66.20 (3) | O3xvi—Mg2—Ba1xix | 138.48 (2) |
O3iii—Ba1—O3v | 123.54 (3) | O3xvii—Mg2—Ba1xix | 48.18 (2) |
O3iv—Ba1—O3v | 93.36 (2) | O3xviii—Mg2—Ba1xix | 131.82 (2) |
O3i—Ba1—O3vi | 66.20 (3) | O3xiii—Mg2—Ba1xx | 81.689 (19) |
O3ii—Ba1—O3vi | 93.36 (2) | O3xiv—Mg2—Ba1xx | 98.311 (19) |
O3iii—Ba1—O3vi | 93.36 (2) | O3xv—Mg2—Ba1xx | 138.48 (2) |
O3iv—Ba1—O3vi | 123.54 (3) | O3xvi—Mg2—Ba1xx | 41.52 (2) |
O3v—Ba1—O3vi | 137.22 (3) | O3xvii—Mg2—Ba1xx | 131.82 (2) |
O3i—Ba1—O3vii | 177.235 (16) | O3xviii—Mg2—Ba1xx | 48.18 (2) |
O3ii—Ba1—O3vii | 57.10 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.89 (2) | O3xiii—Mg2—Ba1xxi | 48.18 (2) |
O3iv—Ba1—O3vii | 85.046 (15) | O3xiv—Mg2—Ba1xxi | 131.82 (2) |
O3v—Ba1—O3vii | 84.496 (15) | O3xv—Mg2—Ba1xxi | 98.311 (19) |
O3vi—Ba1—O3vii | 116.57 (2) | O3xvi—Mg2—Ba1xxi | 81.689 (19) |
O3i—Ba1—O3viii | 57.10 (2) | O3xvii—Mg2—Ba1xxi | 41.52 (2) |
O3ii—Ba1—O3viii | 177.235 (16) | O3xviii—Mg2—Ba1xxi | 138.48 (2) |
O3iii—Ba1—O3viii | 85.046 (15) | Ba1xix—Mg2—Ba1xxi | 77.121 (2) |
O3iv—Ba1—O3viii | 43.89 (2) | Ba1xx—Mg2—Ba1xxi | 102.879 (2) |
O3v—Ba1—O3viii | 116.57 (2) | O3xiii—Mg2—Ba1xxii | 131.82 (2) |
O3vi—Ba1—O3viii | 84.496 (15) | O3xiv—Mg2—Ba1xxii | 48.18 (2) |
O3vii—Ba1—O3viii | 122.41 (2) | O3xv—Mg2—Ba1xxii | 81.689 (19) |
O3i—Ba1—O3ix | 43.89 (2) | O3xvi—Mg2—Ba1xxii | 98.311 (19) |
O3ii—Ba1—O3ix | 84.495 (15) | O3xvii—Mg2—Ba1xxii | 138.48 (2) |
O3iii—Ba1—O3ix | 177.235 (17) | O3xviii—Mg2—Ba1xxii | 41.52 (2) |
O3iv—Ba1—O3ix | 116.57 (2) | Ba1xix—Mg2—Ba1xxii | 102.879 (2) |
O3v—Ba1—O3ix | 57.10 (2) | Ba1xx—Mg2—Ba1xxii | 77.121 (2) |
O3vi—Ba1—O3ix | 85.047 (16) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.15 (2) | O3xiii—Mg2—Ba1xxiii | 41.52 (2) |
O3viii—Ba1—O3ix | 97.031 (17) | O3xiv—Mg2—Ba1xxiii | 138.48 (2) |
O3i—Ba1—O3x | 84.495 (15) | O3xv—Mg2—Ba1xxiii | 48.18 (2) |
O3ii—Ba1—O3x | 43.89 (2) | O3xvi—Mg2—Ba1xxiii | 131.82 (2) |
O3iii—Ba1—O3x | 116.57 (2) | O3xvii—Mg2—Ba1xxiii | 98.312 (19) |
O3iv—Ba1—O3x | 177.235 (17) | O3xviii—Mg2—Ba1xxiii | 81.688 (19) |
O3v—Ba1—O3x | 85.047 (16) | Ba1xix—Mg2—Ba1xxiii | 77.121 (2) |
O3vi—Ba1—O3x | 57.10 (2) | Ba1xx—Mg2—Ba1xxiii | 102.879 (2) |
O3vii—Ba1—O3x | 97.031 (17) | Ba1xxi—Mg2—Ba1xxiii | 77.121 (2) |
O3viii—Ba1—O3x | 135.15 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.879 (2) |
O3ix—Ba1—O3x | 60.67 (3) | O3xiii—Mg2—Ba1iii | 138.48 (2) |
O3i—Ba1—O3xi | 85.046 (15) | O3xiv—Mg2—Ba1iii | 41.52 (2) |
O3ii—Ba1—O3xi | 116.57 (2) | O3xv—Mg2—Ba1iii | 131.82 (2) |
O3iii—Ba1—O3xi | 57.10 (2) | O3xvi—Mg2—Ba1iii | 48.18 (2) |
O3iv—Ba1—O3xi | 84.496 (15) | O3xvii—Mg2—Ba1iii | 81.688 (19) |
O3v—Ba1—O3xi | 177.235 (16) | O3xviii—Mg2—Ba1iii | 98.312 (19) |
O3vi—Ba1—O3xi | 43.89 (2) | Ba1xix—Mg2—Ba1iii | 102.879 (2) |
O3vii—Ba1—O3xi | 97.031 (17) | Ba1xx—Mg2—Ba1iii | 77.121 (2) |
O3viii—Ba1—O3xi | 60.67 (3) | Ba1xxi—Mg2—Ba1iii | 102.879 (2) |
O3ix—Ba1—O3xi | 122.41 (2) | Ba1xxii—Mg2—Ba1iii | 77.121 (2) |
O3x—Ba1—O3xi | 97.031 (17) | Ba1xxiii—Mg2—Ba1iii | 180.0 |
O3i—Ba1—O3xii | 116.57 (2) | C4xxiv—O3—Mg2xxv | 139.37 (6) |
O3ii—Ba1—O3xii | 85.046 (15) | C4xxiv—O3—Ba1iii | 99.64 (4) |
O3iii—Ba1—O3xii | 84.496 (15) | Mg2xxv—O3—Ba1iii | 109.68 (3) |
O3iv—Ba1—O3xii | 57.10 (2) | C4xxiv—O3—Ba1x | 88.94 (4) |
O3v—Ba1—O3xii | 43.89 (2) | Mg2xxv—O3—Ba1x | 101.76 (3) |
O3vi—Ba1—O3xii | 177.235 (16) | Ba1iii—O3—Ba1x | 116.57 (2) |
O3vii—Ba1—O3xii | 60.67 (3) | O3xxvi—C4—O3xxvii | 119.907 (6) |
O3viii—Ba1—O3xii | 97.031 (17) | O3xxvi—C4—O3xxviii | 119.907 (6) |
O3ix—Ba1—O3xii | 97.031 (17) | O3xxvii—C4—O3xxviii | 119.907 (6) |
O3x—Ba1—O3xii | 122.41 (2) | O3xxvi—C4—Ba1xxii | 149.14 (6) |
O3xi—Ba1—O3xii | 135.15 (2) | O3xxvii—C4—Ba1xxii | 68.24 (4) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxviii—C4—Ba1xxii | 57.88 (4) |
O3xiii—Mg2—O3xv | 86.64 (3) | O3xxvi—C4—Ba1xx | 57.88 (4) |
O3xiv—Mg2—O3xv | 93.36 (3) | O3xxvii—C4—Ba1xx | 149.14 (6) |
O3xiii—Mg2—O3xvi | 93.36 (3) | O3xxviii—C4—Ba1xx | 68.24 (4) |
O3xiv—Mg2—O3xvi | 86.64 (3) | Ba1xxii—C4—Ba1xx | 99.053 (18) |
O3xv—Mg2—O3xvi | 180.00 (6) | O3xxvi—C4—Ba1iii | 68.24 (4) |
O3xiii—Mg2—O3xvii | 86.64 (3) | O3xxvii—C4—Ba1iii | 57.88 (4) |
O3xiv—Mg2—O3xvii | 93.36 (3) | O3xxviii—C4—Ba1iii | 149.14 (6) |
O3xv—Mg2—O3xvii | 86.64 (3) | Ba1xxii—C4—Ba1iii | 99.052 (18) |
O3xvi—Mg2—O3xvii | 93.36 (3) | Ba1xx—C4—Ba1iii | 99.052 (18) |
O3xiii—Mg2—O3xviii | 93.36 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.841 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9499 reflections |
a = 5.0180 (1) Å | θ = 1.5–45° |
c = 33.5012 (8) Å | µ = 8.24 mm−1 |
V = 730.55 (3) Å3 | T = 320 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.030 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9499 measured reflections | k = −9→10 |
701 independent reflections | l = −36→66 |
484 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0134P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.023 | (Δ/σ)max < 0.001 |
S = 0.97 | Δρmax = 0.51 e Å−3 |
701 reflections | Δρmin = −0.42 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01119 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00893 (7) | |
O3 | 0.1219 (2) | 0.82952 (19) | 0.12915 (2) | 0.02110 (14) | |
C4 | 0.0000 | 0.0000 | 0.13038 (3) | 0.00949 (11) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.00978 (2) | 0.00978 (2) | 0.01400 (3) | 0.00489 (1) | 0.000 | 0.000 |
Mg2 | 0.00767 (11) | 0.00767 (11) | 0.01146 (17) | 0.00383 (5) | 0.000 | 0.000 |
O3 | 0.0284 (4) | 0.0241 (4) | 0.0227 (2) | 0.0221 (3) | −0.0088 (3) | −0.0053 (3) |
C4 | 0.00917 (17) | 0.00917 (17) | 0.0101 (3) | 0.00459 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8435 (8) | Mg2—O3xviii | 2.0591 (6) |
Ba1—O3ii | 2.8435 (8) | Mg2—Ba1xix | 4.0234 (1) |
Ba1—O3iii | 2.8435 (9) | Mg2—Ba1xx | 4.0234 (1) |
Ba1—O3iv | 2.8435 (9) | Mg2—Ba1xxi | 4.0234 (1) |
Ba1—O3v | 2.8435 (8) | Mg2—Ba1xxii | 4.0234 (1) |
Ba1—O3vi | 2.8435 (8) | Mg2—Ba1iii | 4.0234 (1) |
Ba1—O3vii | 3.0511 (9) | Mg2—Ba1xxiii | 4.0234 (1) |
Ba1—O3viii | 3.0511 (9) | O3—C4xxiv | 1.2771 (6) |
Ba1—O3ix | 3.0511 (9) | O3—Mg2xxv | 2.0592 (6) |
Ba1—O3x | 3.0511 (9) | O3—Ba1iii | 2.8435 (8) |
Ba1—O3xi | 3.0511 (9) | O3—Ba1x | 3.0511 (9) |
Ba1—O3xii | 3.0511 (9) | C4—O3xxvi | 1.2771 (6) |
Mg2—O3xiii | 2.0591 (6) | C4—O3xxvii | 1.2771 (6) |
Mg2—O3xiv | 2.0591 (6) | C4—O3xxviii | 1.2771 (6) |
Mg2—O3xv | 2.0591 (6) | C4—Ba1xxii | 3.2980 (4) |
Mg2—O3xvi | 2.0591 (6) | C4—Ba1xx | 3.2980 (4) |
Mg2—O3xvii | 2.0591 (6) | C4—Ba1iii | 3.2981 (4) |
O3i—Ba1—O3ii | 123.42 (3) | O3xiv—Mg2—O3xviii | 86.63 (3) |
O3i—Ba1—O3iii | 137.12 (3) | O3xv—Mg2—O3xviii | 93.37 (3) |
O3ii—Ba1—O3iii | 93.61 (2) | O3xvi—Mg2—O3xviii | 86.63 (3) |
O3i—Ba1—O3iv | 93.61 (2) | O3xvii—Mg2—O3xviii | 180.00 (5) |
O3ii—Ba1—O3iv | 137.12 (3) | O3xiii—Mg2—Ba1xix | 41.85 (2) |
O3iii—Ba1—O3iv | 65.83 (3) | O3xiv—Mg2—Ba1xix | 138.15 (2) |
O3i—Ba1—O3v | 93.61 (2) | O3xv—Mg2—Ba1xix | 98.35 (2) |
O3ii—Ba1—O3v | 65.83 (3) | O3xvi—Mg2—Ba1xix | 81.65 (2) |
O3iii—Ba1—O3v | 123.42 (3) | O3xvii—Mg2—Ba1xix | 47.86 (3) |
O3iv—Ba1—O3v | 93.61 (2) | O3xviii—Mg2—Ba1xix | 132.14 (3) |
O3i—Ba1—O3vi | 65.83 (3) | O3xiii—Mg2—Ba1xx | 138.15 (2) |
O3ii—Ba1—O3vi | 93.61 (2) | O3xiv—Mg2—Ba1xx | 41.85 (2) |
O3iii—Ba1—O3vi | 93.61 (2) | O3xv—Mg2—Ba1xx | 81.65 (2) |
O3iv—Ba1—O3vi | 123.42 (3) | O3xvi—Mg2—Ba1xx | 98.35 (2) |
O3v—Ba1—O3vi | 137.12 (3) | O3xvii—Mg2—Ba1xx | 132.14 (3) |
O3i—Ba1—O3vii | 177.511 (19) | O3xviii—Mg2—Ba1xx | 47.86 (3) |
O3ii—Ba1—O3vii | 57.15 (2) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.88 (2) | O3xiii—Mg2—Ba1xxi | 98.35 (2) |
O3iv—Ba1—O3vii | 84.957 (16) | O3xiv—Mg2—Ba1xxi | 81.65 (2) |
O3v—Ba1—O3vii | 84.459 (16) | O3xv—Mg2—Ba1xxi | 47.86 (2) |
O3vi—Ba1—O3vii | 116.66 (2) | O3xvi—Mg2—Ba1xxi | 132.14 (2) |
O3i—Ba1—O3viii | 57.15 (2) | O3xvii—Mg2—Ba1xxi | 41.86 (2) |
O3ii—Ba1—O3viii | 177.511 (19) | O3xviii—Mg2—Ba1xxi | 138.14 (2) |
O3iii—Ba1—O3viii | 84.957 (16) | Ba1xix—Mg2—Ba1xxi | 77.159 (1) |
O3iv—Ba1—O3viii | 43.88 (2) | Ba1xx—Mg2—Ba1xxi | 102.841 (1) |
O3v—Ba1—O3viii | 116.66 (2) | O3xiii—Mg2—Ba1xxii | 81.65 (2) |
O3vi—Ba1—O3viii | 84.459 (16) | O3xiv—Mg2—Ba1xxii | 98.35 (2) |
O3vii—Ba1—O3viii | 122.41 (2) | O3xv—Mg2—Ba1xxii | 132.14 (2) |
O3i—Ba1—O3ix | 43.88 (3) | O3xvi—Mg2—Ba1xxii | 47.86 (2) |
O3ii—Ba1—O3ix | 84.458 (16) | O3xvii—Mg2—Ba1xxii | 138.14 (2) |
O3iii—Ba1—O3ix | 177.51 (2) | O3xviii—Mg2—Ba1xxii | 41.86 (2) |
O3iv—Ba1—O3ix | 116.66 (2) | Ba1xix—Mg2—Ba1xxii | 102.841 (1) |
O3v—Ba1—O3ix | 57.15 (2) | Ba1xx—Mg2—Ba1xxii | 77.159 (1) |
O3vi—Ba1—O3ix | 84.958 (16) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.26 (2) | O3xiii—Mg2—Ba1iii | 132.14 (2) |
O3viii—Ba1—O3ix | 96.917 (18) | O3xiv—Mg2—Ba1iii | 47.86 (2) |
O3i—Ba1—O3x | 84.458 (16) | O3xv—Mg2—Ba1iii | 138.14 (2) |
O3ii—Ba1—O3x | 43.88 (3) | O3xvi—Mg2—Ba1iii | 41.86 (2) |
O3iii—Ba1—O3x | 116.66 (2) | O3xvii—Mg2—Ba1iii | 81.64 (2) |
O3iv—Ba1—O3x | 177.51 (2) | O3xviii—Mg2—Ba1iii | 98.36 (2) |
O3v—Ba1—O3x | 84.958 (16) | Ba1xix—Mg2—Ba1iii | 102.841 (1) |
O3vi—Ba1—O3x | 57.15 (2) | Ba1xx—Mg2—Ba1iii | 77.159 (1) |
O3vii—Ba1—O3x | 96.917 (18) | Ba1xxi—Mg2—Ba1iii | 102.841 (1) |
O3viii—Ba1—O3x | 135.26 (2) | Ba1xxii—Mg2—Ba1iii | 77.159 (1) |
O3ix—Ba1—O3x | 60.85 (3) | O3xiii—Mg2—Ba1xxiii | 47.86 (2) |
O3i—Ba1—O3xi | 84.957 (16) | O3xiv—Mg2—Ba1xxiii | 132.14 (2) |
O3ii—Ba1—O3xi | 116.66 (2) | O3xv—Mg2—Ba1xxiii | 41.86 (2) |
O3iii—Ba1—O3xi | 57.15 (2) | O3xvi—Mg2—Ba1xxiii | 138.14 (2) |
O3iv—Ba1—O3xi | 84.459 (16) | O3xvii—Mg2—Ba1xxiii | 98.36 (2) |
O3v—Ba1—O3xi | 177.511 (19) | O3xviii—Mg2—Ba1xxiii | 81.64 (2) |
O3vi—Ba1—O3xi | 43.88 (3) | Ba1xix—Mg2—Ba1xxiii | 77.159 (1) |
O3vii—Ba1—O3xi | 96.916 (18) | Ba1xx—Mg2—Ba1xxiii | 102.841 (1) |
O3viii—Ba1—O3xi | 60.85 (3) | Ba1xxi—Mg2—Ba1xxiii | 77.159 (1) |
O3ix—Ba1—O3xi | 122.41 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.841 (1) |
O3x—Ba1—O3xi | 96.916 (18) | Ba1iii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.66 (2) | C4xxiv—O3—Mg2xxv | 139.51 (6) |
O3ii—Ba1—O3xii | 84.957 (16) | C4xxiv—O3—Ba1iii | 99.20 (5) |
O3iii—Ba1—O3xii | 84.459 (16) | Mg2xxv—O3—Ba1iii | 109.25 (3) |
O3iv—Ba1—O3xii | 57.15 (2) | C4xxiv—O3—Ba1x | 89.54 (5) |
O3v—Ba1—O3xii | 43.88 (3) | Mg2xxv—O3—Ba1x | 102.12 (3) |
O3vi—Ba1—O3xii | 177.511 (19) | Ba1iii—O3—Ba1x | 116.66 (2) |
O3vii—Ba1—O3xii | 60.85 (3) | O3xxvi—C4—O3xxvii | 119.897 (6) |
O3viii—Ba1—O3xii | 96.916 (18) | O3xxvi—C4—O3xxviii | 119.897 (6) |
O3ix—Ba1—O3xii | 96.916 (18) | O3xxvii—C4—O3xxviii | 119.897 (6) |
O3x—Ba1—O3xii | 122.41 (2) | O3xxvi—C4—Ba1xxii | 149.16 (6) |
O3xi—Ba1—O3xii | 135.26 (3) | O3xxvii—C4—Ba1xxii | 67.68 (4) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxviii—C4—Ba1xxii | 58.33 (4) |
O3xiii—Mg2—O3xv | 86.63 (3) | O3xxvi—C4—Ba1xx | 58.33 (4) |
O3xiv—Mg2—O3xv | 93.37 (3) | O3xxvii—C4—Ba1xx | 149.16 (6) |
O3xiii—Mg2—O3xvi | 93.37 (3) | O3xxviii—C4—Ba1xx | 67.68 (4) |
O3xiv—Mg2—O3xvi | 86.63 (3) | Ba1xxii—C4—Ba1xx | 99.062 (17) |
O3xv—Mg2—O3xvi | 180.00 (7) | O3xxvi—C4—Ba1iii | 67.68 (4) |
O3xiii—Mg2—O3xvii | 86.63 (3) | O3xxvii—C4—Ba1iii | 58.33 (4) |
O3xiv—Mg2—O3xvii | 93.37 (3) | O3xxviii—C4—Ba1iii | 149.16 (6) |
O3xv—Mg2—O3xvii | 86.63 (3) | Ba1xxii—C4—Ba1iii | 99.062 (17) |
O3xvi—Mg2—O3xvii | 93.37 (3) | Ba1xx—C4—Ba1iii | 99.062 (17) |
O3xiii—Mg2—O3xviii | 93.37 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) x−1/3, x−y+1/3, z−1/6; (xiv) −x+1/3, −x+y−1/3, −z+1/6; (xv) −x+y−1/3, y−2/3, z−1/6; (xvi) x−y+1/3, −y+2/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.840 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9461 reflections |
a = 5.0183 (1) Å | θ = 1.5–45° |
c = 33.5074 (8) Å | µ = 8.24 mm−1 |
V = 730.78 (3) Å3 | T = 330 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9461 measured reflections | k = −9→10 |
701 independent reflections | l = −34→66 |
477 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.011 | w = 1/[σ2(Fo2) + (0.0138P)2] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.024 | (Δ/σ)max < 0.001 |
S = 1.01 | Δρmax = 0.57 e Å−3 |
701 reflections | Δρmin = −0.41 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01163 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00926 (8) | |
O3 | 0.1239 (2) | 0.8315 (2) | 0.12914 (2) | 0.02222 (15) | |
C4 | 0.0000 | 0.0000 | 0.13038 (3) | 0.00966 (12) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01018 (3) | 0.01018 (3) | 0.01453 (4) | 0.00509 (1) | 0.000 | 0.000 |
Mg2 | 0.00787 (11) | 0.00787 (11) | 0.01206 (18) | 0.00393 (6) | 0.000 | 0.000 |
O3 | 0.0302 (4) | 0.0257 (4) | 0.0235 (2) | 0.0236 (4) | −0.0094 (3) | −0.0057 (3) |
C4 | 0.00945 (18) | 0.00945 (18) | 0.0101 (3) | 0.00473 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8518 (9) | Mg2—O3xviii | 2.0589 (7) |
Ba1—O3ii | 2.8518 (9) | Mg2—Ba1xix | 4.0239 (1) |
Ba1—O3iii | 2.8518 (10) | Mg2—Ba1xx | 4.0239 (1) |
Ba1—O3iv | 2.8518 (10) | Mg2—Ba1xxi | 4.0239 (1) |
Ba1—O3v | 2.8518 (9) | Mg2—Ba1xxii | 4.0239 (1) |
Ba1—O3vi | 2.8518 (9) | Mg2—Ba1iii | 4.0238 (1) |
Ba1—O3vii | 3.0426 (10) | Mg2—Ba1xxiii | 4.0238 (1) |
Ba1—O3viii | 3.0426 (10) | O3—C4xxiv | 1.2766 (7) |
Ba1—O3ix | 3.0426 (10) | O3—Mg2xxv | 2.0589 (7) |
Ba1—O3x | 3.0426 (10) | O3—Ba1iii | 2.8518 (9) |
Ba1—O3xi | 3.0426 (10) | O3—Ba1x | 3.0426 (10) |
Ba1—O3xii | 3.0426 (10) | C4—O3xxvi | 1.2766 (7) |
Mg2—O3xiii | 2.0589 (7) | C4—O3xxvii | 1.2766 (7) |
Mg2—O3xiv | 2.0589 (7) | C4—O3xxviii | 1.2766 (7) |
Mg2—O3xv | 2.0589 (7) | C4—Ba1xxii | 3.2984 (4) |
Mg2—O3xvi | 2.0589 (7) | C4—Ba1xx | 3.2984 (5) |
Mg2—O3xvii | 2.0589 (7) | C4—Ba1iii | 3.2984 (4) |
O3i—Ba1—O3ii | 123.38 (3) | O3xiv—Mg2—O3xviii | 86.58 (3) |
O3i—Ba1—O3iii | 137.02 (3) | O3xv—Mg2—O3xviii | 93.42 (3) |
O3ii—Ba1—O3iii | 93.76 (2) | O3xvi—Mg2—O3xviii | 86.58 (3) |
O3i—Ba1—O3iv | 93.76 (2) | O3xvii—Mg2—O3xviii | 180.00 (5) |
O3ii—Ba1—O3iv | 137.02 (3) | O3xiii—Mg2—Ba1xix | 42.08 (3) |
O3iii—Ba1—O3iv | 65.60 (4) | O3xiv—Mg2—Ba1xix | 137.92 (3) |
O3i—Ba1—O3v | 93.76 (2) | O3xv—Mg2—Ba1xix | 98.33 (2) |
O3ii—Ba1—O3v | 65.60 (3) | O3xvi—Mg2—Ba1xix | 81.67 (2) |
O3iii—Ba1—O3v | 123.38 (3) | O3xvii—Mg2—Ba1xix | 47.60 (3) |
O3iv—Ba1—O3v | 93.76 (2) | O3xviii—Mg2—Ba1xix | 132.40 (3) |
O3i—Ba1—O3vi | 65.60 (3) | O3xiii—Mg2—Ba1xx | 137.92 (3) |
O3ii—Ba1—O3vi | 93.76 (2) | O3xiv—Mg2—Ba1xx | 42.08 (3) |
O3iii—Ba1—O3vi | 93.76 (2) | O3xv—Mg2—Ba1xx | 81.67 (2) |
O3iv—Ba1—O3vi | 123.38 (3) | O3xvi—Mg2—Ba1xx | 98.33 (2) |
O3v—Ba1—O3vi | 137.02 (3) | O3xvii—Mg2—Ba1xx | 132.40 (3) |
O3i—Ba1—O3vii | 177.71 (2) | O3xviii—Mg2—Ba1xx | 47.60 (3) |
O3ii—Ba1—O3vii | 57.14 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.89 (3) | O3xiii—Mg2—Ba1xxi | 98.33 (2) |
O3iv—Ba1—O3vii | 84.922 (17) | O3xiv—Mg2—Ba1xxi | 81.67 (2) |
O3v—Ba1—O3vii | 84.465 (16) | O3xv—Mg2—Ba1xxi | 47.60 (3) |
O3vi—Ba1—O3vii | 116.69 (2) | O3xvi—Mg2—Ba1xxi | 132.40 (3) |
O3i—Ba1—O3viii | 57.14 (3) | O3xvii—Mg2—Ba1xxi | 42.08 (3) |
O3ii—Ba1—O3viii | 177.71 (2) | O3xviii—Mg2—Ba1xxi | 137.92 (3) |
O3iii—Ba1—O3viii | 84.922 (17) | Ba1xix—Mg2—Ba1xxi | 77.154 (1) |
O3iv—Ba1—O3viii | 43.89 (3) | Ba1xx—Mg2—Ba1xxi | 102.846 (1) |
O3v—Ba1—O3viii | 116.69 (2) | O3xiii—Mg2—Ba1xxii | 81.67 (2) |
O3vi—Ba1—O3viii | 84.465 (16) | O3xiv—Mg2—Ba1xxii | 98.33 (2) |
O3vii—Ba1—O3viii | 122.45 (3) | O3xv—Mg2—Ba1xxii | 132.40 (3) |
O3i—Ba1—O3ix | 43.89 (3) | O3xvi—Mg2—Ba1xxii | 47.60 (3) |
O3ii—Ba1—O3ix | 84.465 (16) | O3xvii—Mg2—Ba1xxii | 137.92 (3) |
O3iii—Ba1—O3ix | 177.71 (2) | O3xviii—Mg2—Ba1xxii | 42.08 (3) |
O3iv—Ba1—O3ix | 116.69 (2) | Ba1xix—Mg2—Ba1xxii | 102.846 (1) |
O3v—Ba1—O3ix | 57.13 (3) | Ba1xx—Mg2—Ba1xxii | 77.154 (1) |
O3vi—Ba1—O3ix | 84.923 (17) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.31 (3) | O3xiii—Mg2—Ba1iii | 132.40 (3) |
O3viii—Ba1—O3ix | 96.80 (2) | O3xiv—Mg2—Ba1iii | 47.60 (3) |
O3i—Ba1—O3x | 84.465 (16) | O3xv—Mg2—Ba1iii | 137.92 (3) |
O3ii—Ba1—O3x | 43.89 (3) | O3xvi—Mg2—Ba1iii | 42.08 (3) |
O3iii—Ba1—O3x | 116.69 (2) | O3xvii—Mg2—Ba1iii | 81.67 (2) |
O3iv—Ba1—O3x | 177.71 (2) | O3xviii—Mg2—Ba1iii | 98.33 (2) |
O3v—Ba1—O3x | 84.923 (17) | Ba1xix—Mg2—Ba1iii | 102.847 (2) |
O3vi—Ba1—O3x | 57.13 (3) | Ba1xx—Mg2—Ba1iii | 77.153 (1) |
O3vii—Ba1—O3x | 96.80 (2) | Ba1xxi—Mg2—Ba1iii | 102.847 (1) |
O3viii—Ba1—O3x | 135.31 (3) | Ba1xxii—Mg2—Ba1iii | 77.153 (1) |
O3ix—Ba1—O3x | 61.03 (3) | O3xiii—Mg2—Ba1xxiii | 47.60 (3) |
O3i—Ba1—O3xi | 84.923 (17) | O3xiv—Mg2—Ba1xxiii | 132.40 (3) |
O3ii—Ba1—O3xi | 116.69 (2) | O3xv—Mg2—Ba1xxiii | 42.08 (3) |
O3iii—Ba1—O3xi | 57.13 (3) | O3xvi—Mg2—Ba1xxiii | 137.92 (3) |
O3iv—Ba1—O3xi | 84.465 (16) | O3xvii—Mg2—Ba1xxiii | 98.33 (2) |
O3v—Ba1—O3xi | 177.71 (2) | O3xviii—Mg2—Ba1xxiii | 81.67 (2) |
O3vi—Ba1—O3xi | 43.89 (3) | Ba1xix—Mg2—Ba1xxiii | 77.153 (1) |
O3vii—Ba1—O3xi | 96.80 (2) | Ba1xx—Mg2—Ba1xxiii | 102.847 (2) |
O3viii—Ba1—O3xi | 61.03 (3) | Ba1xxi—Mg2—Ba1xxiii | 77.153 (1) |
O3ix—Ba1—O3xi | 122.45 (3) | Ba1xxii—Mg2—Ba1xxiii | 102.847 (1) |
O3x—Ba1—O3xi | 96.80 (2) | Ba1iii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.69 (2) | C4xxiv—O3—Mg2xxv | 139.62 (7) |
O3ii—Ba1—O3xii | 84.923 (17) | C4xxiv—O3—Ba1iii | 98.82 (5) |
O3iii—Ba1—O3xii | 84.465 (16) | Mg2xxv—O3—Ba1iii | 108.98 (3) |
O3iv—Ba1—O3xii | 57.13 (3) | C4xxiv—O3—Ba1x | 89.94 (5) |
O3v—Ba1—O3xii | 43.89 (3) | Mg2xxv—O3—Ba1x | 102.42 (3) |
O3vi—Ba1—O3xii | 177.71 (2) | Ba1iii—O3—Ba1x | 116.68 (2) |
O3vii—Ba1—O3xii | 61.03 (3) | O3xxvi—C4—O3xxvii | 119.894 (7) |
O3viii—Ba1—O3xii | 96.80 (2) | O3xxvi—C4—O3xxviii | 119.894 (7) |
O3ix—Ba1—O3xii | 96.80 (2) | O3xxvii—C4—O3xxviii | 119.894 (6) |
O3x—Ba1—O3xii | 122.45 (3) | O3xxvi—C4—Ba1xxii | 149.19 (6) |
O3xi—Ba1—O3xii | 135.31 (3) | O3xxvii—C4—Ba1xxii | 67.29 (5) |
O3xiii—Mg2—O3xiv | 180.00 (4) | O3xxviii—C4—Ba1xxii | 58.69 (5) |
O3xiii—Mg2—O3xv | 86.59 (3) | O3xxvi—C4—Ba1xx | 58.69 (5) |
O3xiv—Mg2—O3xv | 93.41 (3) | O3xxvii—C4—Ba1xx | 149.19 (6) |
O3xiii—Mg2—O3xvi | 93.41 (3) | O3xxviii—C4—Ba1xx | 67.29 (5) |
O3xiv—Mg2—O3xvi | 86.59 (3) | Ba1xxii—C4—Ba1xx | 99.056 (18) |
O3xv—Mg2—O3xvi | 180.00 (7) | O3xxvi—C4—Ba1iii | 67.29 (5) |
O3xiii—Mg2—O3xvii | 86.58 (3) | O3xxvii—C4—Ba1iii | 58.69 (5) |
O3xiv—Mg2—O3xvii | 93.42 (3) | O3xxviii—C4—Ba1iii | 149.20 (6) |
O3xv—Mg2—O3xvii | 86.58 (3) | Ba1xxii—C4—Ba1iii | 99.055 (18) |
O3xvi—Mg2—O3xvii | 93.42 (3) | Ba1xx—C4—Ba1iii | 99.055 (18) |
O3xiii—Mg2—O3xviii | 93.42 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) x−1/3, x−y+1/3, z−1/6; (xiv) −x+1/3, −x+y−1/3, −z+1/6; (xv) −x+y−1/3, y−2/3, z−1/6; (xvi) x−y+1/3, −y+2/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.837 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9472 reflections |
a = 5.0187 (1) Å | θ = 1.5–45° |
c = 33.5273 (9) Å | µ = 8.23 mm−1 |
V = 731.33 (4) Å3 | T = 340 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9472 measured reflections | k = −9→10 |
700 independent reflections | l = −34→66 |
474 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.011 | w = 1/[σ2(Fo2) + (0.0119P)2 + 0.6958P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.025 | (Δ/σ)max < 0.001 |
S = 0.98 | Δρmax = 0.77 e Å−3 |
700 reflections | Δρmin = −0.55 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01198 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00956 (8) | |
O3 | 0.1256 (3) | 0.8333 (3) | 0.12912 (2) | 0.02315 (17) | |
C4 | 0.0000 | 0.0000 | 0.13035 (3) | 0.00997 (13) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01049 (3) | 0.01049 (3) | 0.01495 (4) | 0.00524 (1) | 0.000 | 0.000 |
Mg2 | 0.00826 (12) | 0.00826 (12) | 0.0122 (2) | 0.00413 (6) | 0.000 | 0.000 |
O3 | 0.0325 (5) | 0.0262 (4) | 0.0244 (3) | 0.0249 (4) | −0.0103 (4) | −0.0062 (4) |
C4 | 0.00959 (19) | 0.00959 (19) | 0.0107 (3) | 0.00479 (10) | 0.000 | 0.000 |
Ba1—O3i | 2.8598 (11) | Mg2—O3xviii | 2.0594 (7) |
Ba1—O3ii | 2.8598 (11) | Mg2—Ba1xix | 4.0252 (1) |
Ba1—O3iii | 2.8598 (11) | Mg2—Ba1xx | 4.0252 (1) |
Ba1—O3iv | 2.8598 (11) | Mg2—Ba1xxi | 4.0252 (1) |
Ba1—O3v | 2.8598 (11) | Mg2—Ba1xxii | 4.0252 (1) |
Ba1—O3vi | 2.8598 (11) | Mg2—Ba1iii | 4.0252 (1) |
Ba1—O3vii | 3.0355 (12) | Mg2—Ba1xxiii | 4.0252 (1) |
Ba1—O3viii | 3.0355 (12) | O3—C4xxiv | 1.2755 (7) |
Ba1—O3ix | 3.0355 (12) | O3—Mg2xxv | 2.0595 (7) |
Ba1—O3x | 3.0355 (12) | O3—Ba1iii | 2.8597 (11) |
Ba1—O3xi | 3.0355 (12) | O3—Ba1x | 3.0354 (12) |
Ba1—O3xii | 3.0355 (12) | C4—O3xxvi | 1.2755 (7) |
Mg2—O3xiii | 2.0594 (7) | C4—O3xxvii | 1.2755 (7) |
Mg2—O3xiv | 2.0594 (7) | C4—O3xxviii | 1.2755 (7) |
Mg2—O3xv | 2.0594 (7) | C4—Ba1xxii | 3.2985 (5) |
Mg2—O3xvi | 2.0594 (7) | C4—Ba1xx | 3.2985 (5) |
Mg2—O3xvii | 2.0594 (7) | C4—Ba1iii | 3.2985 (5) |
O3i—Ba1—O3ii | 123.33 (3) | O3xiv—Mg2—O3xviii | 86.55 (3) |
O3i—Ba1—O3iii | 136.97 (3) | O3xv—Mg2—O3xviii | 93.45 (3) |
O3ii—Ba1—O3iii | 93.88 (3) | O3xvi—Mg2—O3xviii | 86.55 (3) |
O3i—Ba1—O3iv | 93.88 (3) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 136.97 (3) | O3xiii—Mg2—Ba1xix | 42.29 (3) |
O3iii—Ba1—O3iv | 65.43 (4) | O3xiv—Mg2—Ba1xix | 137.71 (3) |
O3i—Ba1—O3v | 93.88 (3) | O3xv—Mg2—Ba1xix | 98.31 (2) |
O3ii—Ba1—O3v | 65.43 (4) | O3xvi—Mg2—Ba1xix | 81.69 (2) |
O3iii—Ba1—O3v | 123.33 (3) | O3xvii—Mg2—Ba1xix | 47.37 (3) |
O3iv—Ba1—O3v | 93.88 (3) | O3xviii—Mg2—Ba1xix | 132.63 (3) |
O3i—Ba1—O3vi | 65.43 (4) | O3xiii—Mg2—Ba1xx | 137.71 (3) |
O3ii—Ba1—O3vi | 93.88 (3) | O3xiv—Mg2—Ba1xx | 42.29 (3) |
O3iii—Ba1—O3vi | 93.88 (3) | O3xv—Mg2—Ba1xx | 81.69 (2) |
O3iv—Ba1—O3vi | 123.33 (3) | O3xvi—Mg2—Ba1xx | 98.31 (2) |
O3v—Ba1—O3vi | 136.97 (3) | O3xvii—Mg2—Ba1xx | 132.63 (3) |
O3i—Ba1—O3vii | 177.89 (3) | O3xviii—Mg2—Ba1xx | 47.37 (3) |
O3ii—Ba1—O3vii | 57.14 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.87 (3) | O3xiii—Mg2—Ba1xxi | 98.31 (2) |
O3iv—Ba1—O3vii | 84.910 (18) | O3xiv—Mg2—Ba1xxi | 81.69 (2) |
O3v—Ba1—O3vii | 84.489 (17) | O3xv—Mg2—Ba1xxi | 47.37 (3) |
O3vi—Ba1—O3vii | 116.68 (3) | O3xvi—Mg2—Ba1xxi | 132.63 (3) |
O3i—Ba1—O3viii | 57.14 (3) | O3xvii—Mg2—Ba1xxi | 42.29 (3) |
O3ii—Ba1—O3viii | 177.89 (3) | O3xviii—Mg2—Ba1xxi | 137.71 (3) |
O3iii—Ba1—O3viii | 84.910 (18) | Ba1xix—Mg2—Ba1xxi | 77.131 (2) |
O3iv—Ba1—O3viii | 43.87 (3) | Ba1xx—Mg2—Ba1xxi | 102.869 (2) |
O3v—Ba1—O3viii | 116.68 (3) | O3xiii—Mg2—Ba1xxii | 81.69 (2) |
O3vi—Ba1—O3viii | 84.489 (17) | O3xiv—Mg2—Ba1xxii | 98.31 (2) |
O3vii—Ba1—O3viii | 122.48 (3) | O3xv—Mg2—Ba1xxii | 132.63 (3) |
O3i—Ba1—O3ix | 43.87 (3) | O3xvi—Mg2—Ba1xxii | 47.37 (3) |
O3ii—Ba1—O3ix | 84.488 (17) | O3xvii—Mg2—Ba1xxii | 137.71 (3) |
O3iii—Ba1—O3ix | 177.89 (3) | O3xviii—Mg2—Ba1xxii | 42.29 (3) |
O3iv—Ba1—O3ix | 116.68 (3) | Ba1xix—Mg2—Ba1xxii | 102.869 (2) |
O3v—Ba1—O3ix | 57.14 (3) | Ba1xx—Mg2—Ba1xxii | 77.131 (2) |
O3vi—Ba1—O3ix | 84.911 (18) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.39 (3) | O3xiii—Mg2—Ba1iii | 132.63 (3) |
O3viii—Ba1—O3ix | 96.68 (2) | O3xiv—Mg2—Ba1iii | 47.37 (3) |
O3i—Ba1—O3x | 84.488 (17) | O3xv—Mg2—Ba1iii | 137.71 (3) |
O3ii—Ba1—O3x | 43.87 (3) | O3xvi—Mg2—Ba1iii | 42.29 (3) |
O3iii—Ba1—O3x | 116.68 (3) | O3xvii—Mg2—Ba1iii | 81.69 (2) |
O3iv—Ba1—O3x | 177.89 (3) | O3xviii—Mg2—Ba1iii | 98.31 (2) |
O3v—Ba1—O3x | 84.911 (18) | Ba1xix—Mg2—Ba1iii | 102.869 (1) |
O3vi—Ba1—O3x | 57.14 (3) | Ba1xx—Mg2—Ba1iii | 77.131 (1) |
O3vii—Ba1—O3x | 96.68 (2) | Ba1xxi—Mg2—Ba1iii | 102.869 (2) |
O3viii—Ba1—O3x | 135.39 (3) | Ba1xxii—Mg2—Ba1iii | 77.131 (2) |
O3ix—Ba1—O3x | 61.22 (3) | O3xiii—Mg2—Ba1xxiii | 47.37 (3) |
O3i—Ba1—O3xi | 84.911 (18) | O3xiv—Mg2—Ba1xxiii | 132.63 (3) |
O3ii—Ba1—O3xi | 116.68 (3) | O3xv—Mg2—Ba1xxiii | 42.29 (3) |
O3iii—Ba1—O3xi | 57.14 (3) | O3xvi—Mg2—Ba1xxiii | 137.71 (3) |
O3iv—Ba1—O3xi | 84.489 (17) | O3xvii—Mg2—Ba1xxiii | 98.31 (2) |
O3v—Ba1—O3xi | 177.89 (3) | O3xviii—Mg2—Ba1xxiii | 81.69 (2) |
O3vi—Ba1—O3xi | 43.87 (3) | Ba1xix—Mg2—Ba1xxiii | 77.131 (1) |
O3vii—Ba1—O3xi | 96.68 (2) | Ba1xx—Mg2—Ba1xxiii | 102.869 (1) |
O3viii—Ba1—O3xi | 61.22 (3) | Ba1xxi—Mg2—Ba1xxiii | 77.131 (2) |
O3ix—Ba1—O3xi | 122.48 (3) | Ba1xxii—Mg2—Ba1xxiii | 102.869 (2) |
O3x—Ba1—O3xi | 96.68 (2) | Ba1iii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.68 (3) | C4xxiv—O3—Mg2xxv | 139.75 (7) |
O3ii—Ba1—O3xii | 84.911 (18) | C4xxiv—O3—Ba1iii | 98.47 (6) |
O3iii—Ba1—O3xii | 84.489 (17) | Mg2xxv—O3—Ba1iii | 108.73 (4) |
O3iv—Ba1—O3xii | 57.14 (3) | C4xxiv—O3—Ba1x | 90.29 (6) |
O3v—Ba1—O3xii | 43.87 (3) | Mg2xxv—O3—Ba1x | 102.69 (4) |
O3vi—Ba1—O3xii | 177.89 (3) | Ba1iii—O3—Ba1x | 116.68 (3) |
O3vii—Ba1—O3xii | 61.22 (3) | O3xxvi—C4—O3xxvii | 119.898 (7) |
O3viii—Ba1—O3xii | 96.68 (2) | O3xxvi—C4—O3xxviii | 119.898 (7) |
O3ix—Ba1—O3xii | 96.68 (2) | O3xxvii—C4—O3xxviii | 119.898 (7) |
O3x—Ba1—O3xii | 122.48 (3) | O3xxvi—C4—Ba1xxii | 149.29 (7) |
O3xi—Ba1—O3xii | 135.39 (3) | O3xxvii—C4—Ba1xxii | 66.96 (6) |
O3xiii—Mg2—O3xiv | 180.00 (8) | O3xxviii—C4—Ba1xxii | 59.04 (5) |
O3xiii—Mg2—O3xv | 86.55 (3) | O3xxvi—C4—Ba1xx | 59.04 (5) |
O3xiv—Mg2—O3xv | 93.45 (3) | O3xxvii—C4—Ba1xx | 149.29 (7) |
O3xiii—Mg2—O3xvi | 93.45 (3) | O3xxviii—C4—Ba1xx | 66.96 (6) |
O3xiv—Mg2—O3xvi | 86.55 (3) | Ba1xxii—C4—Ba1xx | 99.06 (2) |
O3xv—Mg2—O3xvi | 180.00 (9) | O3xxvi—C4—Ba1iii | 66.96 (6) |
O3xiii—Mg2—O3xvii | 86.55 (3) | O3xxvii—C4—Ba1iii | 59.04 (5) |
O3xiv—Mg2—O3xvii | 93.45 (3) | O3xxviii—C4—Ba1iii | 149.29 (7) |
O3xv—Mg2—O3xvii | 86.55 (3) | Ba1xxii—C4—Ba1iii | 99.06 (2) |
O3xvi—Mg2—O3xvii | 93.45 (3) | Ba1xx—C4—Ba1iii | 99.06 (2) |
O3xiii—Mg2—O3xviii | 93.45 (3) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) x−1/3, x−y+1/3, z−1/6; (xiv) −x+1/3, −x+y−1/3, −z+1/6; (xv) −x+y−1/3, y−2/3, z−1/6; (xvi) x−y+1/3, −y+2/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −y+1, x−y+1, z; (xxvii) −x+y−1, −x, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.837 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 9486 reflections |
a = 5.0198 (1) Å | θ = 1.5–45° |
c = 33.5169 (9) Å | µ = 8.23 mm−1 |
V = 731.42 (4) Å3 | T = 350 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.030 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→9 |
9486 measured reflections | k = −9→10 |
701 independent reflections | l = −34→66 |
459 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.010 | w = 1/[σ2(Fo2) + (0.0114P)2 + 0.365P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.024 | (Δ/σ)max < 0.001 |
S = 1.01 | Δρmax = 0.64 e Å−3 |
701 reflections | Δρmin = −0.46 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01230 (2) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.00981 (8) | |
O3 | 0.1288 (3) | 0.8363 (3) | 0.12909 (2) | 0.02438 (18) | |
C4 | 0.0000 | 0.0000 | 0.13033 (3) | 0.01030 (12) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01078 (3) | 0.01078 (3) | 0.01534 (4) | 0.00539 (1) | 0.000 | 0.000 |
Mg2 | 0.00841 (11) | 0.00841 (11) | 0.01260 (19) | 0.00420 (6) | 0.000 | 0.000 |
O3 | 0.0347 (6) | 0.0286 (5) | 0.0248 (2) | 0.0270 (4) | −0.0110 (5) | −0.0070 (4) |
C4 | 0.00994 (19) | 0.00994 (19) | 0.0110 (3) | 0.00497 (9) | 0.000 | 0.000 |
Ba1—O3i | 2.8724 (13) | Mg2—O3xviii | 2.0588 (7) |
Ba1—O3ii | 2.8724 (13) | Mg2—Ba1xix | 4.0251 (1) |
Ba1—O3iii | 2.8724 (13) | Mg2—Ba1xx | 4.0251 (1) |
Ba1—O3iv | 2.8724 (13) | Mg2—Ba1xxi | 4.0251 (1) |
Ba1—O3v | 2.8724 (13) | Mg2—Ba1xxii | 4.0251 (1) |
Ba1—O3vi | 2.8724 (13) | Mg2—Ba1xxiii | 4.0251 (1) |
Ba1—O3vii | 3.0216 (14) | Mg2—Ba1i | 4.0251 (1) |
Ba1—O3viii | 3.0216 (14) | O3—C4xxiv | 1.2756 (7) |
Ba1—O3ix | 3.0216 (14) | O3—Mg2xxv | 2.0588 (7) |
Ba1—O3x | 3.0216 (14) | O3—Ba1i | 2.8724 (13) |
Ba1—O3xi | 3.0216 (14) | O3—Ba1x | 3.0216 (14) |
Ba1—O3xii | 3.0216 (14) | C4—O3xxvi | 1.2756 (7) |
Mg2—O3xiii | 2.0587 (7) | C4—O3xxvii | 1.2756 (7) |
Mg2—O3xiv | 2.0587 (7) | C4—O3xxviii | 1.2756 (7) |
Mg2—O3xv | 2.0587 (7) | C4—Ba1xxii | 3.2985 (5) |
Mg2—O3xvi | 2.0587 (7) | C4—Ba1xx | 3.2985 (5) |
Mg2—O3xvii | 2.0588 (7) | C4—Ba1i | 3.2985 (5) |
O3i—Ba1—O3ii | 136.79 (3) | O3xiv—Mg2—O3xviii | 86.48 (3) |
O3i—Ba1—O3iii | 123.27 (3) | O3xv—Mg2—O3xviii | 93.52 (3) |
O3ii—Ba1—O3iii | 94.16 (3) | O3xvi—Mg2—O3xviii | 86.48 (3) |
O3i—Ba1—O3iv | 65.02 (4) | O3xvii—Mg2—O3xviii | 180.00 (7) |
O3ii—Ba1—O3iv | 94.16 (3) | O3xiii—Mg2—Ba1xix | 98.29 (2) |
O3iii—Ba1—O3iv | 94.16 (3) | O3xiv—Mg2—Ba1xix | 81.71 (2) |
O3i—Ba1—O3v | 94.16 (3) | O3xv—Mg2—Ba1xix | 42.66 (4) |
O3ii—Ba1—O3v | 123.27 (3) | O3xvi—Mg2—Ba1xix | 137.34 (4) |
O3iii—Ba1—O3v | 65.02 (4) | O3xvii—Mg2—Ba1xix | 46.97 (4) |
O3iv—Ba1—O3v | 136.79 (3) | O3xviii—Mg2—Ba1xix | 133.03 (4) |
O3i—Ba1—O3vi | 94.16 (3) | O3xiii—Mg2—Ba1xx | 81.71 (2) |
O3ii—Ba1—O3vi | 65.02 (4) | O3xiv—Mg2—Ba1xx | 98.29 (2) |
O3iii—Ba1—O3vi | 136.79 (3) | O3xv—Mg2—Ba1xx | 137.34 (4) |
O3iv—Ba1—O3vi | 123.27 (3) | O3xvi—Mg2—Ba1xx | 42.66 (4) |
O3v—Ba1—O3vi | 94.16 (3) | O3xvii—Mg2—Ba1xx | 133.03 (4) |
O3i—Ba1—O3vii | 178.21 (3) | O3xviii—Mg2—Ba1xx | 46.97 (4) |
O3ii—Ba1—O3vii | 43.92 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 57.12 (3) | O3xiii—Mg2—Ba1xxi | 46.97 (4) |
O3iv—Ba1—O3vii | 116.77 (3) | O3xiv—Mg2—Ba1xxi | 133.03 (4) |
O3v—Ba1—O3vii | 84.467 (17) | O3xv—Mg2—Ba1xxi | 98.29 (2) |
O3vi—Ba1—O3vii | 84.823 (18) | O3xvi—Mg2—Ba1xxi | 81.71 (2) |
O3i—Ba1—O3viii | 43.92 (3) | O3xvii—Mg2—Ba1xxi | 42.66 (4) |
O3ii—Ba1—O3viii | 178.21 (3) | O3xviii—Mg2—Ba1xxi | 137.34 (4) |
O3iii—Ba1—O3viii | 84.467 (17) | Ba1xix—Mg2—Ba1xxi | 77.154 (1) |
O3iv—Ba1—O3viii | 84.823 (17) | Ba1xx—Mg2—Ba1xxi | 102.846 (1) |
O3v—Ba1—O3viii | 57.12 (3) | O3xiii—Mg2—Ba1xxii | 133.03 (4) |
O3vi—Ba1—O3viii | 116.77 (3) | O3xiv—Mg2—Ba1xxii | 46.97 (4) |
O3vii—Ba1—O3viii | 135.45 (3) | O3xv—Mg2—Ba1xxii | 81.71 (2) |
O3i—Ba1—O3ix | 57.12 (3) | O3xvi—Mg2—Ba1xxii | 98.29 (2) |
O3ii—Ba1—O3ix | 84.823 (17) | O3xvii—Mg2—Ba1xxii | 137.34 (4) |
O3iii—Ba1—O3ix | 178.21 (3) | O3xviii—Mg2—Ba1xxii | 42.66 (4) |
O3iv—Ba1—O3ix | 84.467 (17) | Ba1xix—Mg2—Ba1xxii | 102.846 (1) |
O3v—Ba1—O3ix | 116.77 (3) | Ba1xx—Mg2—Ba1xxii | 77.154 (1) |
O3vi—Ba1—O3ix | 43.92 (3) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 122.55 (3) | O3xiii—Mg2—Ba1xxiii | 42.66 (4) |
O3viii—Ba1—O3ix | 96.53 (2) | O3xiv—Mg2—Ba1xxiii | 137.34 (4) |
O3i—Ba1—O3x | 116.77 (3) | O3xv—Mg2—Ba1xxiii | 46.97 (4) |
O3ii—Ba1—O3x | 84.467 (17) | O3xvi—Mg2—Ba1xxiii | 133.03 (4) |
O3iii—Ba1—O3x | 84.823 (17) | O3xvii—Mg2—Ba1xxiii | 98.30 (2) |
O3iv—Ba1—O3x | 178.21 (3) | O3xviii—Mg2—Ba1xxiii | 81.70 (2) |
O3v—Ba1—O3x | 43.92 (3) | Ba1xix—Mg2—Ba1xxiii | 77.154 (2) |
O3vi—Ba1—O3x | 57.12 (3) | Ba1xx—Mg2—Ba1xxiii | 102.846 (2) |
O3vii—Ba1—O3x | 61.45 (4) | Ba1xxi—Mg2—Ba1xxiii | 77.154 (2) |
O3viii—Ba1—O3x | 96.53 (2) | Ba1xxii—Mg2—Ba1xxiii | 102.846 (1) |
O3ix—Ba1—O3x | 96.53 (2) | O3xiii—Mg2—Ba1i | 137.34 (4) |
O3i—Ba1—O3xi | 84.823 (17) | O3xiv—Mg2—Ba1i | 42.66 (4) |
O3ii—Ba1—O3xi | 57.12 (3) | O3xv—Mg2—Ba1i | 133.03 (4) |
O3iii—Ba1—O3xi | 116.77 (3) | O3xvi—Mg2—Ba1i | 46.97 (4) |
O3iv—Ba1—O3xi | 43.92 (3) | O3xvii—Mg2—Ba1i | 81.70 (2) |
O3v—Ba1—O3xi | 178.21 (3) | O3xviii—Mg2—Ba1i | 98.30 (2) |
O3vi—Ba1—O3xi | 84.467 (17) | Ba1xix—Mg2—Ba1i | 102.846 (2) |
O3vii—Ba1—O3xi | 96.53 (2) | Ba1xx—Mg2—Ba1i | 77.154 (2) |
O3viii—Ba1—O3xi | 122.55 (3) | Ba1xxi—Mg2—Ba1i | 102.846 (1) |
O3ix—Ba1—O3xi | 61.45 (4) | Ba1xxii—Mg2—Ba1i | 77.154 (2) |
O3x—Ba1—O3xi | 135.45 (3) | Ba1xxiii—Mg2—Ba1i | 180.0 |
O3i—Ba1—O3xii | 84.467 (17) | C4xxiv—O3—Mg2xxv | 139.89 (7) |
O3ii—Ba1—O3xii | 116.77 (3) | C4xxiv—O3—Ba1i | 97.86 (7) |
O3iii—Ba1—O3xii | 43.92 (3) | Mg2xxv—O3—Ba1i | 108.29 (5) |
O3iv—Ba1—O3xii | 57.12 (3) | C4xxiv—O3—Ba1x | 90.91 (7) |
O3v—Ba1—O3xii | 84.823 (17) | Mg2xxv—O3—Ba1x | 103.15 (5) |
O3vi—Ba1—O3xii | 178.21 (3) | Ba1i—O3—Ba1x | 116.77 (3) |
O3vii—Ba1—O3xii | 96.53 (2) | O3xxvi—C4—O3xxvii | 119.896 (7) |
O3viii—Ba1—O3xii | 61.45 (4) | O3xxvi—C4—O3xxviii | 119.896 (7) |
O3ix—Ba1—O3xii | 135.45 (3) | O3xxvii—C4—O3xxviii | 119.893 (7) |
O3x—Ba1—O3xii | 122.55 (3) | O3xxvi—C4—Ba1xxii | 59.61 (6) |
O3xi—Ba1—O3xii | 96.53 (2) | O3xxvii—C4—Ba1xxii | 149.38 (7) |
O3xiii—Mg2—O3xiv | 180.00 (9) | O3xxviii—C4—Ba1xxii | 66.34 (6) |
O3xiii—Mg2—O3xv | 86.49 (3) | O3xxvi—C4—Ba1xx | 66.34 (7) |
O3xiv—Mg2—O3xv | 93.51 (3) | O3xxvii—C4—Ba1xx | 59.61 (6) |
O3xiii—Mg2—O3xvi | 93.51 (3) | O3xxviii—C4—Ba1xx | 149.38 (7) |
O3xiv—Mg2—O3xvi | 86.49 (3) | Ba1xxii—C4—Ba1xx | 99.090 (19) |
O3xv—Mg2—O3xvi | 180.00 (9) | O3xxvi—C4—Ba1i | 149.38 (7) |
O3xiii—Mg2—O3xvii | 86.48 (3) | O3xxvii—C4—Ba1i | 66.34 (6) |
O3xiv—Mg2—O3xvii | 93.52 (3) | O3xxviii—C4—Ba1i | 59.61 (6) |
O3xv—Mg2—O3xvii | 86.48 (3) | Ba1xxii—C4—Ba1i | 99.090 (19) |
O3xvi—Mg2—O3xvii | 93.52 (3) | Ba1xx—C4—Ba1i | 99.090 (19) |
O3xiii—Mg2—O3xviii | 93.52 (3) |
Symmetry codes: (i) −x−1/3, −y+1/3, −z+1/3; (ii) −x+y−2/3, y−1/3, z+1/6; (iii) x+1/3, x−y+2/3, z+1/6; (iv) −y+1/3, −x−1/3, z+1/6; (v) y−1/3, −x+y−2/3, −z+1/3; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) −y+4/3, −x+2/3, z+1/6; (viii) x−y+2/3, x−2/3, −z+1/3; (ix) y−4/3, −x+y−2/3, −z+1/3; (x) −x+2/3, −y+4/3, −z+1/3; (xi) x−2/3, x−y+2/3, z+1/6; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) −x+y−1/3, y−2/3, z−1/6; (xiv) x−y+1/3, −y+2/3, −z+1/6; (xv) x−1/3, x−y+1/3, z−1/6; (xvi) −x+1/3, −x+y−1/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) x, y−1, z; (xxvii) −y+1, x−y+1, z; (xxviii) −x+y−1, −x, z. |
C6Ba3Mg3O18 | Dx = 3.834 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3c | Cell parameters from 5541 reflections |
a = 5.0206 (1) Å | θ = 1.5–45° |
c = 33.5307 (14) Å | µ = 8.22 mm−1 |
V = 731.95 (4) Å3 | T = 360 K |
Z = 2 | Prismatic |
F(000) = 768 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.027 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −10→8 |
5541 measured reflections | k = −8→10 |
701 independent reflections | l = −34→66 |
444 reflections with I > 2σ(I) |
Refinement on F2 | 17 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.012 | w = 1/[σ2(Fo2) + (0.0128P)2 + 0.6467P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.028 | (Δ/σ)max < 0.001 |
S = 0.99 | Δρmax = 0.76 e Å−3 |
701 reflections | Δρmin = −0.72 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.2500 | 0.01269 (3) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01003 (9) | |
O3 | 0.1326 (4) | 0.8401 (4) | 0.12905 (3) | 0.0253 (2) | |
C4 | 0.0000 | 0.0000 | 0.13031 (4) | 0.01021 (15) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01117 (3) | 0.01117 (3) | 0.01572 (5) | 0.00558 (2) | 0.000 | 0.000 |
Mg2 | 0.00870 (14) | 0.00870 (14) | 0.0127 (2) | 0.00435 (7) | 0.000 | 0.000 |
O3 | 0.0359 (8) | 0.0301 (6) | 0.0256 (3) | 0.0282 (5) | −0.0121 (7) | −0.0077 (6) |
C4 | 0.0099 (2) | 0.0099 (2) | 0.0109 (4) | 0.00493 (11) | 0.000 | 0.000 |
Ba1—O3i | 2.8884 (19) | Mg2—O3xviii | 2.0595 (8) |
Ba1—O3ii | 2.8884 (19) | Mg2—Ba1xix | 4.0262 (1) |
Ba1—O3iii | 2.8884 (19) | Mg2—Ba1xx | 4.0262 (1) |
Ba1—O3iv | 2.8884 (19) | Mg2—Ba1xxi | 4.0262 (1) |
Ba1—O3v | 2.8884 (19) | Mg2—Ba1xxii | 4.0262 (1) |
Ba1—O3vi | 2.8884 (19) | Mg2—Ba1iii | 4.0262 (1) |
Ba1—O3vii | 3.005 (2) | Mg2—Ba1xxiii | 4.0262 (1) |
Ba1—O3viii | 3.005 (2) | O3—C4xxiv | 1.2747 (8) |
Ba1—O3ix | 3.005 (2) | O3—Mg2xxv | 2.0595 (8) |
Ba1—O3x | 3.005 (2) | O3—Ba1iii | 2.8884 (19) |
Ba1—O3xi | 3.005 (2) | O3—Ba1x | 3.005 (2) |
Ba1—O3xii | 3.005 (2) | C4—O3xxvi | 1.2747 (8) |
Mg2—O3xiii | 2.0595 (8) | C4—O3xxvii | 1.2747 (8) |
Mg2—O3xiv | 2.0595 (8) | C4—O3xxviii | 1.2747 (8) |
Mg2—O3xv | 2.0595 (8) | C4—Ba1xxii | 3.2990 (6) |
Mg2—O3xvi | 2.0595 (8) | C4—Ba1xx | 3.2990 (6) |
Mg2—O3xvii | 2.0595 (8) | C4—Ba1iii | 3.2990 (6) |
O3i—Ba1—O3ii | 123.17 (3) | O3xiv—Mg2—O3xviii | 86.40 (4) |
O3i—Ba1—O3iii | 136.62 (4) | O3xv—Mg2—O3xviii | 93.60 (4) |
O3ii—Ba1—O3iii | 94.46 (4) | O3xvi—Mg2—O3xviii | 86.40 (4) |
O3i—Ba1—O3iv | 94.46 (4) | O3xvii—Mg2—O3xviii | 180.00 (9) |
O3ii—Ba1—O3iv | 136.62 (4) | O3xiii—Mg2—Ba1xix | 43.10 (5) |
O3iii—Ba1—O3iv | 64.57 (6) | O3xiv—Mg2—Ba1xix | 136.90 (5) |
O3i—Ba1—O3v | 94.46 (4) | O3xv—Mg2—Ba1xix | 98.25 (3) |
O3ii—Ba1—O3v | 64.57 (6) | O3xvi—Mg2—Ba1xix | 81.75 (3) |
O3iii—Ba1—O3v | 123.17 (3) | O3xvii—Mg2—Ba1xix | 46.48 (6) |
O3iv—Ba1—O3v | 94.45 (4) | O3xviii—Mg2—Ba1xix | 133.52 (6) |
O3i—Ba1—O3vi | 64.57 (6) | O3xiii—Mg2—Ba1xx | 136.90 (5) |
O3ii—Ba1—O3vi | 94.46 (4) | O3xiv—Mg2—Ba1xx | 43.10 (5) |
O3iii—Ba1—O3vi | 94.45 (4) | O3xv—Mg2—Ba1xx | 81.75 (3) |
O3iv—Ba1—O3vi | 123.17 (3) | O3xvi—Mg2—Ba1xx | 98.25 (3) |
O3v—Ba1—O3vi | 136.62 (4) | O3xvii—Mg2—Ba1xx | 133.52 (6) |
O3i—Ba1—O3vii | 178.61 (4) | O3xviii—Mg2—Ba1xx | 46.48 (6) |
O3ii—Ba1—O3vii | 57.13 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.92 (3) | O3xiii—Mg2—Ba1xxi | 98.25 (3) |
O3iv—Ba1—O3vii | 84.75 (2) | O3xiv—Mg2—Ba1xxi | 81.75 (3) |
O3v—Ba1—O3vii | 84.47 (2) | O3xv—Mg2—Ba1xxi | 46.47 (6) |
O3vi—Ba1—O3vii | 116.82 (3) | O3xvi—Mg2—Ba1xxi | 133.53 (6) |
O3i—Ba1—O3viii | 57.13 (3) | O3xvii—Mg2—Ba1xxi | 43.10 (5) |
O3ii—Ba1—O3viii | 178.61 (4) | O3xviii—Mg2—Ba1xxi | 136.90 (5) |
O3iii—Ba1—O3viii | 84.75 (2) | Ba1xix—Mg2—Ba1xxi | 77.143 (2) |
O3iv—Ba1—O3viii | 43.92 (3) | Ba1xx—Mg2—Ba1xxi | 102.857 (2) |
O3v—Ba1—O3viii | 116.82 (3) | O3xiii—Mg2—Ba1xxii | 81.75 (3) |
O3vi—Ba1—O3viii | 84.47 (2) | O3xiv—Mg2—Ba1xxii | 98.25 (3) |
O3vii—Ba1—O3viii | 122.61 (3) | O3xv—Mg2—Ba1xxii | 133.53 (6) |
O3i—Ba1—O3ix | 43.92 (3) | O3xvi—Mg2—Ba1xxii | 46.47 (6) |
O3ii—Ba1—O3ix | 84.47 (2) | O3xvii—Mg2—Ba1xxii | 136.90 (5) |
O3iii—Ba1—O3ix | 178.61 (5) | O3xviii—Mg2—Ba1xxii | 43.10 (5) |
O3iv—Ba1—O3ix | 116.82 (3) | Ba1xix—Mg2—Ba1xxii | 102.857 (2) |
O3v—Ba1—O3ix | 57.13 (3) | Ba1xx—Mg2—Ba1xxii | 77.143 (2) |
O3vi—Ba1—O3ix | 84.75 (2) | Ba1xxi—Mg2—Ba1xxii | 180.0 |
O3vii—Ba1—O3ix | 135.58 (3) | O3xiii—Mg2—Ba1iii | 133.52 (6) |
O3viii—Ba1—O3ix | 96.31 (3) | O3xiv—Mg2—Ba1iii | 46.48 (6) |
O3i—Ba1—O3x | 84.47 (2) | O3xv—Mg2—Ba1iii | 136.90 (5) |
O3ii—Ba1—O3x | 43.92 (3) | O3xvi—Mg2—Ba1iii | 43.10 (5) |
O3iii—Ba1—O3x | 116.82 (3) | O3xvii—Mg2—Ba1iii | 81.75 (3) |
O3iv—Ba1—O3x | 178.61 (5) | O3xviii—Mg2—Ba1iii | 98.25 (3) |
O3v—Ba1—O3x | 84.75 (2) | Ba1xix—Mg2—Ba1iii | 102.857 (2) |
O3vi—Ba1—O3x | 57.13 (3) | Ba1xx—Mg2—Ba1iii | 77.143 (2) |
O3vii—Ba1—O3x | 96.31 (3) | Ba1xxi—Mg2—Ba1iii | 102.857 (2) |
O3viii—Ba1—O3x | 135.58 (3) | Ba1xxii—Mg2—Ba1iii | 77.143 (2) |
O3ix—Ba1—O3x | 61.78 (5) | O3xiii—Mg2—Ba1xxiii | 46.48 (6) |
O3i—Ba1—O3xi | 84.75 (2) | O3xiv—Mg2—Ba1xxiii | 133.52 (6) |
O3ii—Ba1—O3xi | 116.82 (3) | O3xv—Mg2—Ba1xxiii | 43.10 (5) |
O3iii—Ba1—O3xi | 57.13 (3) | O3xvi—Mg2—Ba1xxiii | 136.90 (5) |
O3iv—Ba1—O3xi | 84.47 (2) | O3xvii—Mg2—Ba1xxiii | 98.25 (3) |
O3v—Ba1—O3xi | 178.61 (4) | O3xviii—Mg2—Ba1xxiii | 81.75 (3) |
O3vi—Ba1—O3xi | 43.92 (3) | Ba1xix—Mg2—Ba1xxiii | 77.143 (2) |
O3vii—Ba1—O3xi | 96.31 (3) | Ba1xx—Mg2—Ba1xxiii | 102.857 (2) |
O3viii—Ba1—O3xi | 61.78 (5) | Ba1xxi—Mg2—Ba1xxiii | 77.143 (2) |
O3ix—Ba1—O3xi | 122.61 (3) | Ba1xxii—Mg2—Ba1xxiii | 102.857 (2) |
O3x—Ba1—O3xi | 96.31 (3) | Ba1iii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.82 (3) | C4xxiv—O3—Mg2xxv | 139.99 (8) |
O3ii—Ba1—O3xii | 84.75 (2) | C4xxiv—O3—Ba1iii | 97.15 (9) |
O3iii—Ba1—O3xii | 84.47 (2) | Mg2xxv—O3—Ba1iii | 107.74 (7) |
O3iv—Ba1—O3xii | 57.13 (3) | C4xxiv—O3—Ba1x | 91.71 (10) |
O3v—Ba1—O3xii | 43.92 (3) | Mg2xxv—O3—Ba1x | 103.73 (7) |
O3vi—Ba1—O3xii | 178.61 (4) | Ba1iii—O3—Ba1x | 116.82 (3) |
O3vii—Ba1—O3xii | 61.78 (5) | O3xxvi—C4—O3xxvii | 119.889 (8) |
O3viii—Ba1—O3xii | 96.31 (3) | O3xxvi—C4—O3xxviii | 119.889 (8) |
O3ix—Ba1—O3xii | 96.31 (3) | O3xxvii—C4—O3xxviii | 119.889 (9) |
O3x—Ba1—O3xii | 122.61 (3) | O3xxvi—C4—Ba1xxii | 65.57 (9) |
O3xi—Ba1—O3xii | 135.58 (3) | O3xxvii—C4—Ba1xxii | 149.42 (8) |
O3xiii—Mg2—O3xiv | 180.00 (14) | O3xxviii—C4—Ba1xxii | 60.31 (9) |
O3xiii—Mg2—O3xv | 86.40 (4) | O3xxvi—C4—Ba1xx | 149.42 (8) |
O3xiv—Mg2—O3xv | 93.60 (4) | O3xxvii—C4—Ba1xx | 60.31 (9) |
O3xiii—Mg2—O3xvi | 93.60 (4) | O3xxviii—C4—Ba1xx | 65.57 (9) |
O3xiv—Mg2—O3xvi | 86.40 (4) | Ba1xxii—C4—Ba1xx | 99.09 (2) |
O3xv—Mg2—O3xvi | 180.00 (13) | O3xxvi—C4—Ba1iii | 60.31 (9) |
O3xiii—Mg2—O3xvii | 86.40 (4) | O3xxvii—C4—Ba1iii | 65.57 (9) |
O3xiv—Mg2—O3xvii | 93.60 (4) | O3xxviii—C4—Ba1iii | 149.42 (8) |
O3xv—Mg2—O3xvii | 86.40 (4) | Ba1xxii—C4—Ba1iii | 99.09 (2) |
O3xvi—Mg2—O3xvii | 93.60 (4) | Ba1xx—C4—Ba1iii | 99.09 (2) |
O3xiii—Mg2—O3xviii | 93.60 (4) |
Symmetry codes: (i) −x+y−2/3, y−1/3, z+1/6; (ii) y−1/3, −x+y−2/3, −z+1/3; (iii) −x−1/3, −y+1/3, −z+1/3; (iv) −y+1/3, −x−1/3, z+1/6; (v) x+1/3, x−y+2/3, z+1/6; (vi) x−y+2/3, x+1/3, −z+1/3; (vii) x−y+2/3, x−2/3, −z+1/3; (viii) x−2/3, x−y+2/3, z+1/6; (ix) −y+4/3, −x+2/3, z+1/6; (x) −x+2/3, −y+4/3, −z+1/3; (xi) y−4/3, −x+y−2/3, −z+1/3; (xii) −x+y−2/3, y−4/3, z+1/6; (xiii) x−1/3, x−y+1/3, z−1/6; (xiv) −x+1/3, −x+y−1/3, −z+1/6; (xv) −x+y−1/3, y−2/3, z−1/6; (xvi) x−y+1/3, −y+2/3, −z+1/6; (xvii) −y+2/3, −x+1/3, z−1/6; (xviii) y−2/3, x−1/3, −z+1/6; (xix) x−2/3, y−1/3, z−1/3; (xx) −x+2/3, −y+1/3, −z+1/3; (xxi) x+1/3, y+2/3, z−1/3; (xxii) −x−1/3, −y−2/3, −z+1/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x, y+1, z; (xxv) y+1/3, x+2/3, −z+1/6; (xxvi) −x+y−1, −x, z; (xxvii) −y+1, x−y+1, z; (xxviii) x, y−1, z. |
C6Ba3Mg3O18 | Dx = 3.837 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 5014 reflections |
a = 5.0209 (1) Å | θ = 1.5–45° |
c = 16.7515 (5) Å | µ = 8.23 mm−1 |
V = 365.72 (2) Å3 | T = 370 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.026 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.7° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
5014 measured reflections | k = −10→9 |
428 independent reflections | l = −17→33 |
428 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.014 | w = 1/[σ2(Fo2) + (0.0123P)2 + 0.8639P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.033 | (Δ/σ)max < 0.001 |
S = 1.17 | Δρmax = 1.12 e Å−3 |
428 reflections | Δρmin = −0.72 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01328 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01049 (15) | |
O3 | 0.85354 (13) | 0.7071 (3) | 0.25778 (8) | 0.0267 (2) | |
C4 | 0.0000 | 0.0000 | 0.26072 (11) | 0.0109 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01148 (5) | 0.01148 (5) | 0.01687 (7) | 0.00574 (2) | 0.000 | 0.000 |
Mg2 | 0.0088 (2) | 0.0088 (2) | 0.0138 (4) | 0.00441 (11) | 0.000 | 0.000 |
O3 | 0.0351 (5) | 0.0097 (3) | 0.0269 (5) | 0.00484 (17) | 0.00210 (16) | 0.0042 (3) |
C4 | 0.0105 (4) | 0.0105 (4) | 0.0116 (5) | 0.00525 (18) | 0.000 | 0.000 |
Ba1—O3i | 2.9433 (7) | Mg2—O3xviii | 2.0598 (11) |
Ba1—O3ii | 2.9433 (7) | Mg2—Ba1xix | 4.0246 (1) |
Ba1—O3iii | 2.9433 (7) | Mg2—Ba1xx | 4.0246 (1) |
Ba1—O3iv | 2.9433 (7) | Mg2—Ba1xvi | 4.0246 (1) |
Ba1—O3v | 2.9433 (7) | Mg2—Ba1xxi | 4.0246 (1) |
Ba1—O3vi | 2.9433 (7) | Mg2—Ba1xxii | 4.0247 (1) |
Ba1—O3vii | 2.9433 (7) | Mg2—Ba1xxiii | 4.0247 (1) |
Ba1—O3viii | 2.9433 (7) | O3—C4xxiv | 1.2747 (11) |
Ba1—O3ix | 2.9433 (7) | O3—Mg2xxv | 2.0598 (11) |
Ba1—O3x | 2.9433 (7) | O3—Ba1xix | 2.9433 (7) |
Ba1—O3xi | 2.9433 (7) | O3—Ba1xxvi | 2.9433 (7) |
Ba1—O3xii | 2.9433 (7) | C4—O3xxvii | 1.2746 (11) |
Mg2—O3xiii | 2.0598 (11) | C4—O3xxviii | 1.2746 (11) |
Mg2—O3xiv | 2.0598 (11) | C4—O3xxix | 1.2746 (11) |
Mg2—O3xv | 2.0598 (11) | C4—Ba1xvi | 3.2993 (9) |
Mg2—O3xvi | 2.0598 (11) | C4—Ba1xix | 3.2993 (9) |
Mg2—O3xvii | 2.0598 (11) | C4—Ba1xxii | 3.2993 (9) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.20 (5) |
O3i—Ba1—O3iii | 57.13 (4) | O3xv—Mg2—O3xviii | 93.80 (5) |
O3ii—Ba1—O3iii | 122.87 (4) | O3xvi—Mg2—O3xviii | 86.20 (5) |
O3i—Ba1—O3iv | 122.87 (4) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 57.13 (4) | O3xiii—Mg2—Ba1xix | 44.734 (17) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.266 (17) |
O3i—Ba1—O3v | 44.02 (4) | O3xv—Mg2—Ba1xix | 98.17 (4) |
O3ii—Ba1—O3v | 135.98 (4) | O3xvi—Mg2—Ba1xix | 81.83 (4) |
O3iii—Ba1—O3v | 95.54 (3) | O3xvii—Mg2—Ba1xix | 44.736 (17) |
O3iv—Ba1—O3v | 84.46 (3) | O3xviii—Mg2—Ba1xix | 135.264 (17) |
O3i—Ba1—O3vi | 135.98 (4) | O3xiii—Mg2—Ba1xx | 135.266 (17) |
O3ii—Ba1—O3vi | 44.02 (4) | O3xiv—Mg2—Ba1xx | 44.734 (17) |
O3iii—Ba1—O3vi | 84.46 (3) | O3xv—Mg2—Ba1xx | 81.83 (4) |
O3iv—Ba1—O3vi | 95.54 (3) | O3xvi—Mg2—Ba1xx | 98.17 (4) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 135.264 (17) |
O3i—Ba1—O3vii | 95.54 (3) | O3xviii—Mg2—Ba1xx | 44.736 (17) |
O3ii—Ba1—O3vii | 84.46 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 44.02 (4) | O3xiii—Mg2—Ba1xvi | 98.17 (4) |
O3iv—Ba1—O3vii | 135.98 (4) | O3xiv—Mg2—Ba1xvi | 81.83 (4) |
O3v—Ba1—O3vii | 117.07 (4) | O3xv—Mg2—Ba1xvi | 44.734 (17) |
O3vi—Ba1—O3vii | 62.93 (4) | O3xvi—Mg2—Ba1xvi | 135.266 (17) |
O3i—Ba1—O3viii | 84.46 (3) | O3xvii—Mg2—Ba1xvi | 44.736 (17) |
O3ii—Ba1—O3viii | 95.54 (3) | O3xviii—Mg2—Ba1xvi | 135.264 (17) |
O3iii—Ba1—O3viii | 135.98 (4) | Ba1xix—Mg2—Ba1xvi | 77.184 (2) |
O3iv—Ba1—O3viii | 44.02 (4) | Ba1xx—Mg2—Ba1xvi | 102.816 (2) |
O3v—Ba1—O3viii | 62.93 (4) | O3xiii—Mg2—Ba1xxi | 81.83 (4) |
O3vi—Ba1—O3viii | 117.07 (4) | O3xiv—Mg2—Ba1xxi | 98.17 (4) |
O3vii—Ba1—O3viii | 180.00 (2) | O3xv—Mg2—Ba1xxi | 135.266 (17) |
O3i—Ba1—O3ix | 95.54 (3) | O3xvi—Mg2—Ba1xxi | 44.734 (17) |
O3ii—Ba1—O3ix | 84.46 (3) | O3xvii—Mg2—Ba1xxi | 135.264 (17) |
O3iii—Ba1—O3ix | 117.07 (4) | O3xviii—Mg2—Ba1xxi | 44.736 (17) |
O3iv—Ba1—O3ix | 62.93 (4) | Ba1xix—Mg2—Ba1xxi | 102.816 (2) |
O3v—Ba1—O3ix | 57.13 (4) | Ba1xx—Mg2—Ba1xxi | 77.184 (2) |
O3vi—Ba1—O3ix | 122.87 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 95.54 (3) | O3xiii—Mg2—Ba1xxii | 44.736 (17) |
O3viii—Ba1—O3ix | 84.46 (3) | O3xiv—Mg2—Ba1xxii | 135.264 (17) |
O3i—Ba1—O3x | 84.46 (3) | O3xv—Mg2—Ba1xxii | 44.736 (17) |
O3ii—Ba1—O3x | 95.54 (3) | O3xvi—Mg2—Ba1xxii | 135.264 (17) |
O3iii—Ba1—O3x | 62.93 (4) | O3xvii—Mg2—Ba1xxii | 98.17 (4) |
O3iv—Ba1—O3x | 117.07 (4) | O3xviii—Mg2—Ba1xxii | 81.83 (4) |
O3v—Ba1—O3x | 122.87 (4) | Ba1xix—Mg2—Ba1xxii | 77.184 (1) |
O3vi—Ba1—O3x | 57.13 (4) | Ba1xx—Mg2—Ba1xxii | 102.816 (2) |
O3vii—Ba1—O3x | 84.46 (3) | Ba1xvi—Mg2—Ba1xxii | 77.184 (2) |
O3viii—Ba1—O3x | 95.54 (3) | Ba1xxi—Mg2—Ba1xxii | 102.816 (2) |
O3ix—Ba1—O3x | 180.0 | O3xiii—Mg2—Ba1xxiii | 135.264 (17) |
O3i—Ba1—O3xi | 62.93 (4) | O3xiv—Mg2—Ba1xxiii | 44.736 (17) |
O3ii—Ba1—O3xi | 117.07 (4) | O3xv—Mg2—Ba1xxiii | 135.264 (17) |
O3iii—Ba1—O3xi | 84.46 (3) | O3xvi—Mg2—Ba1xxiii | 44.736 (17) |
O3iv—Ba1—O3xi | 95.54 (3) | O3xvii—Mg2—Ba1xxiii | 81.83 (4) |
O3v—Ba1—O3xi | 84.46 (3) | O3xviii—Mg2—Ba1xxiii | 98.17 (4) |
O3vi—Ba1—O3xi | 95.54 (3) | Ba1xix—Mg2—Ba1xxiii | 102.816 (2) |
O3vii—Ba1—O3xi | 122.87 (4) | Ba1xx—Mg2—Ba1xxiii | 77.184 (1) |
O3viii—Ba1—O3xi | 57.13 (4) | Ba1xvi—Mg2—Ba1xxiii | 102.816 (2) |
O3ix—Ba1—O3xi | 135.98 (5) | Ba1xxi—Mg2—Ba1xxiii | 77.184 (2) |
O3x—Ba1—O3xi | 44.02 (4) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 117.07 (4) | C4xxiv—O3—Mg2xxv | 139.88 (12) |
O3ii—Ba1—O3xii | 62.93 (4) | C4xxiv—O3—Ba1xix | 94.57 (5) |
O3iii—Ba1—O3xii | 95.54 (3) | Mg2xxv—O3—Ba1xix | 105.76 (3) |
O3iv—Ba1—O3xii | 84.46 (3) | C4xxiv—O3—Ba1xxvi | 94.57 (5) |
O3v—Ba1—O3xii | 95.54 (3) | Mg2xxv—O3—Ba1xxvi | 105.76 (3) |
O3vi—Ba1—O3xii | 84.46 (3) | Ba1xix—O3—Ba1xxvi | 117.06 (4) |
O3vii—Ba1—O3xii | 57.13 (4) | O3xxvii—C4—O3xxviii | 119.852 (14) |
O3viii—Ba1—O3xii | 122.87 (4) | O3xxvii—C4—O3xxix | 119.852 (14) |
O3ix—Ba1—O3xii | 44.02 (4) | O3xxviii—C4—O3xxix | 119.852 (14) |
O3x—Ba1—O3xii | 135.98 (5) | O3xxvii—C4—Ba1xvi | 62.78 (5) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xvi | 149.26 (12) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxix—C4—Ba1xvi | 62.78 (5) |
O3xiii—Mg2—O3xv | 86.20 (5) | O3xxvii—C4—Ba1xix | 149.26 (12) |
O3xiv—Mg2—O3xv | 93.80 (5) | O3xxviii—C4—Ba1xix | 62.78 (5) |
O3xiii—Mg2—O3xvi | 93.80 (5) | O3xxix—C4—Ba1xix | 62.78 (5) |
O3xiv—Mg2—O3xvi | 86.20 (5) | Ba1xvi—C4—Ba1xix | 99.09 (4) |
O3xv—Mg2—O3xvi | 180.00 (7) | O3xxvii—C4—Ba1xxii | 62.78 (5) |
O3xiii—Mg2—O3xvii | 86.20 (5) | O3xxviii—C4—Ba1xxii | 62.78 (5) |
O3xiv—Mg2—O3xvii | 93.80 (5) | O3xxix—C4—Ba1xxii | 149.26 (12) |
O3xv—Mg2—O3xvii | 86.20 (5) | Ba1xvi—C4—Ba1xxii | 99.09 (4) |
O3xvi—Mg2—O3xvii | 93.80 (5) | Ba1xix—C4—Ba1xxii | 99.09 (4) |
O3xiii—Mg2—O3xviii | 93.80 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.826 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 5028 reflections |
a = 5.0214 (2) Å | θ = 1.5–45° |
c = 16.7931 (6) Å | µ = 8.21 mm−1 |
V = 366.70 (3) Å3 | T = 380 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 3.6° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
5028 measured reflections | k = −10→9 |
427 independent reflections | l = −32→17 |
427 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.015 | w = 1/[σ2(Fo2) + (0.0098P)2 + 0.8518P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.030 | (Δ/σ)max < 0.001 |
S = 1.14 | Δρmax = 1.22 e Å−3 |
427 reflections | Δρmin = −0.56 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01337 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01058 (14) | |
O3 | 0.85362 (12) | 0.7072 (2) | 0.25778 (7) | 0.0268 (2) | |
C4 | 0.0000 | 0.0000 | 0.26077 (10) | 0.0109 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01179 (4) | 0.01179 (4) | 0.01654 (6) | 0.00590 (2) | 0.000 | 0.000 |
Mg2 | 0.0090 (2) | 0.0090 (2) | 0.0137 (3) | 0.00450 (10) | 0.000 | 0.000 |
O3 | 0.0356 (5) | 0.0100 (3) | 0.0263 (4) | 0.00499 (16) | 0.00209 (15) | 0.0042 (3) |
C4 | 0.0107 (3) | 0.0107 (3) | 0.0113 (5) | 0.00533 (16) | 0.000 | 0.000 |
Ba1—O3i | 2.9455 (6) | Mg2—O3xviii | 2.0625 (10) |
Ba1—O3ii | 2.9455 (6) | Mg2—Ba1xix | 4.0297 (1) |
Ba1—O3iii | 2.9455 (6) | Mg2—Ba1xx | 4.0297 (1) |
Ba1—O3iv | 2.9455 (6) | Mg2—Ba1xvi | 4.0297 (1) |
Ba1—O3v | 2.9455 (6) | Mg2—Ba1xxi | 4.0297 (1) |
Ba1—O3vi | 2.9455 (6) | Mg2—Ba1xxii | 4.0297 (1) |
Ba1—O3vii | 2.9455 (6) | Mg2—Ba1xxiii | 4.0297 (1) |
Ba1—O3viii | 2.9455 (6) | O3—C4xxiv | 1.2741 (11) |
Ba1—O3ix | 2.9455 (6) | O3—Mg2xxv | 2.0624 (10) |
Ba1—O3x | 2.9455 (6) | O3—Ba1xix | 2.9455 (6) |
Ba1—O3xi | 2.9455 (6) | O3—Ba1xxvi | 2.9456 (6) |
Ba1—O3xii | 2.9455 (6) | C4—O3xxvii | 1.2741 (11) |
Mg2—O3xiii | 2.0624 (10) | C4—O3xxviii | 1.2741 (11) |
Mg2—O3xiv | 2.0624 (10) | C4—O3xxix | 1.2741 (11) |
Mg2—O3xv | 2.0624 (10) | C4—Ba1xvi | 3.3019 (8) |
Mg2—O3xvi | 2.0624 (10) | C4—Ba1xix | 3.3019 (8) |
Mg2—O3xvii | 2.0625 (10) | C4—Ba1xxii | 3.3019 (8) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.12 (5) |
O3i—Ba1—O3iii | 43.96 (4) | O3xv—Mg2—O3xviii | 93.88 (5) |
O3ii—Ba1—O3iii | 136.04 (4) | O3xvi—Mg2—O3xviii | 86.12 (5) |
O3i—Ba1—O3iv | 136.04 (4) | O3xvii—Mg2—O3xviii | 180.00 (5) |
O3ii—Ba1—O3iv | 43.96 (4) | O3xiii—Mg2—Ba1xix | 44.692 (15) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.308 (15) |
O3i—Ba1—O3v | 57.12 (4) | O3xv—Mg2—Ba1xix | 98.04 (3) |
O3ii—Ba1—O3v | 122.88 (4) | O3xvi—Mg2—Ba1xix | 81.96 (3) |
O3iii—Ba1—O3v | 95.46 (3) | O3xvii—Mg2—Ba1xix | 44.694 (15) |
O3iv—Ba1—O3v | 84.54 (3) | O3xviii—Mg2—Ba1xix | 135.306 (15) |
O3i—Ba1—O3vi | 122.88 (4) | O3xiii—Mg2—Ba1xx | 135.308 (15) |
O3ii—Ba1—O3vi | 57.12 (4) | O3xiv—Mg2—Ba1xx | 44.692 (15) |
O3iii—Ba1—O3vi | 84.54 (3) | O3xv—Mg2—Ba1xx | 81.96 (3) |
O3iv—Ba1—O3vi | 95.46 (3) | O3xvi—Mg2—Ba1xx | 98.04 (3) |
O3v—Ba1—O3vi | 180.00 (4) | O3xvii—Mg2—Ba1xx | 135.306 (15) |
O3i—Ba1—O3vii | 116.94 (4) | O3xviii—Mg2—Ba1xx | 44.694 (15) |
O3ii—Ba1—O3vii | 63.06 (4) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 95.46 (3) | O3xiii—Mg2—Ba1xvi | 98.04 (3) |
O3iv—Ba1—O3vii | 84.54 (3) | O3xiv—Mg2—Ba1xvi | 81.96 (3) |
O3v—Ba1—O3vii | 95.46 (3) | O3xv—Mg2—Ba1xvi | 44.692 (15) |
O3vi—Ba1—O3vii | 84.54 (3) | O3xvi—Mg2—Ba1xvi | 135.308 (15) |
O3i—Ba1—O3viii | 63.06 (4) | O3xvii—Mg2—Ba1xvi | 44.694 (15) |
O3ii—Ba1—O3viii | 116.94 (4) | O3xviii—Mg2—Ba1xvi | 135.306 (15) |
O3iii—Ba1—O3viii | 84.54 (3) | Ba1xix—Mg2—Ba1xvi | 77.079 (2) |
O3iv—Ba1—O3viii | 95.46 (3) | Ba1xx—Mg2—Ba1xvi | 102.921 (2) |
O3v—Ba1—O3viii | 84.54 (3) | O3xiii—Mg2—Ba1xxi | 81.96 (3) |
O3vi—Ba1—O3viii | 95.46 (3) | O3xiv—Mg2—Ba1xxi | 98.04 (3) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xxi | 135.308 (15) |
O3i—Ba1—O3ix | 84.54 (3) | O3xvi—Mg2—Ba1xxi | 44.692 (15) |
O3ii—Ba1—O3ix | 95.46 (3) | O3xvii—Mg2—Ba1xxi | 135.306 (15) |
O3iii—Ba1—O3ix | 63.06 (4) | O3xviii—Mg2—Ba1xxi | 44.694 (15) |
O3iv—Ba1—O3ix | 116.94 (4) | Ba1xix—Mg2—Ba1xxi | 102.921 (2) |
O3v—Ba1—O3ix | 136.04 (4) | Ba1xx—Mg2—Ba1xxi | 77.079 (2) |
O3vi—Ba1—O3ix | 43.96 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 122.88 (4) | O3xiii—Mg2—Ba1xxii | 44.695 (15) |
O3viii—Ba1—O3ix | 57.12 (4) | O3xiv—Mg2—Ba1xxii | 135.305 (15) |
O3i—Ba1—O3x | 95.46 (3) | O3xv—Mg2—Ba1xxii | 44.695 (15) |
O3ii—Ba1—O3x | 84.54 (3) | O3xvi—Mg2—Ba1xxii | 135.305 (15) |
O3iii—Ba1—O3x | 57.12 (4) | O3xvii—Mg2—Ba1xxii | 98.04 (3) |
O3iv—Ba1—O3x | 122.88 (4) | O3xviii—Mg2—Ba1xxii | 81.96 (3) |
O3v—Ba1—O3x | 116.94 (4) | Ba1xix—Mg2—Ba1xxii | 77.079 (2) |
O3vi—Ba1—O3x | 63.06 (4) | Ba1xx—Mg2—Ba1xxii | 102.921 (2) |
O3vii—Ba1—O3x | 43.96 (4) | Ba1xvi—Mg2—Ba1xxii | 77.079 (2) |
O3viii—Ba1—O3x | 136.04 (4) | Ba1xxi—Mg2—Ba1xxii | 102.921 (2) |
O3ix—Ba1—O3x | 84.54 (3) | O3xiii—Mg2—Ba1xxiii | 135.305 (15) |
O3i—Ba1—O3xi | 95.46 (3) | O3xiv—Mg2—Ba1xxiii | 44.695 (15) |
O3ii—Ba1—O3xi | 84.54 (3) | O3xv—Mg2—Ba1xxiii | 135.305 (15) |
O3iii—Ba1—O3xi | 116.94 (4) | O3xvi—Mg2—Ba1xxiii | 44.695 (15) |
O3iv—Ba1—O3xi | 63.06 (4) | O3xvii—Mg2—Ba1xxiii | 81.96 (3) |
O3v—Ba1—O3xi | 43.96 (4) | O3xviii—Mg2—Ba1xxiii | 98.04 (3) |
O3vi—Ba1—O3xi | 136.04 (4) | Ba1xix—Mg2—Ba1xxiii | 102.921 (2) |
O3vii—Ba1—O3xi | 57.12 (4) | Ba1xx—Mg2—Ba1xxiii | 77.079 (2) |
O3viii—Ba1—O3xi | 122.88 (4) | Ba1xvi—Mg2—Ba1xxiii | 102.921 (2) |
O3ix—Ba1—O3xi | 180.0 | Ba1xxi—Mg2—Ba1xxiii | 77.079 (2) |
O3x—Ba1—O3xi | 95.46 (3) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 84.54 (3) | C4xxiv—O3—Mg2xxv | 139.78 (11) |
O3ii—Ba1—O3xii | 95.46 (3) | C4xxiv—O3—Ba1xix | 94.61 (5) |
O3iii—Ba1—O3xii | 122.88 (4) | Mg2xxv—O3—Ba1xix | 105.80 (3) |
O3iv—Ba1—O3xii | 57.12 (4) | C4xxiv—O3—Ba1xxvi | 94.61 (5) |
O3v—Ba1—O3xii | 63.06 (4) | Mg2xxv—O3—Ba1xxvi | 105.80 (3) |
O3vi—Ba1—O3xii | 116.94 (4) | Ba1xix—O3—Ba1xxvi | 116.94 (4) |
O3vii—Ba1—O3xii | 136.04 (4) | O3xxvii—C4—O3xxviii | 119.847 (13) |
O3viii—Ba1—O3xii | 43.96 (4) | O3xxvii—C4—O3xxix | 119.847 (13) |
O3ix—Ba1—O3xii | 95.46 (3) | O3xxviii—C4—O3xxix | 119.844 (13) |
O3x—Ba1—O3xii | 180.0 | O3xxvii—C4—Ba1xvi | 62.77 (4) |
O3xi—Ba1—O3xii | 84.54 (3) | O3xxviii—C4—Ba1xvi | 62.77 (4) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxix—C4—Ba1xvi | 149.14 (11) |
O3xiii—Mg2—O3xv | 86.12 (5) | O3xxvii—C4—Ba1xix | 62.77 (4) |
O3xiv—Mg2—O3xv | 93.88 (5) | O3xxviii—C4—Ba1xix | 149.14 (11) |
O3xiii—Mg2—O3xvi | 93.88 (5) | O3xxix—C4—Ba1xix | 62.77 (4) |
O3xiv—Mg2—O3xvi | 86.12 (5) | Ba1xvi—C4—Ba1xix | 99.00 (3) |
O3xv—Mg2—O3xvi | 180.00 (7) | O3xxvii—C4—Ba1xxii | 149.14 (11) |
O3xiii—Mg2—O3xvii | 86.12 (5) | O3xxviii—C4—Ba1xxii | 62.77 (4) |
O3xiv—Mg2—O3xvii | 93.88 (5) | O3xxix—C4—Ba1xxii | 62.77 (4) |
O3xv—Mg2—O3xvii | 86.12 (5) | Ba1xvi—C4—Ba1xxii | 99.00 (3) |
O3xvi—Mg2—O3xvii | 93.88 (5) | Ba1xix—C4—Ba1xxii | 99.00 (3) |
O3xiii—Mg2—O3xviii | 93.88 (5) |
Symmetry codes: (i) x−y−2/3, x−4/3, −z+2/3; (ii) −x+y+2/3, −x+4/3, z+1/3; (iii) −x+1/3, −y+2/3, −z+2/3; (iv) x−1/3, y−2/3, z+1/3; (v) y−2/3, −x+y−1/3, −z+2/3; (vi) −y+2/3, x−y+1/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) x−4/3, y−2/3, z+1/3; (x) y−2/3, −x+y+2/3, −z+2/3; (xi) −x+4/3, −y+2/3, −z+2/3; (xii) −y+2/3, x−y−2/3, z+1/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) −x+y, −x+1, z; (xxviii) x−1, y−1, z; (xxix) −y+1, x−y, z. |
C6Ba3Mg3O18 | Dx = 3.829 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 5088 reflections |
a = 5.0206 (2) Å | θ = 1.5–45° |
c = 16.7875 (6) Å | µ = 8.21 mm−1 |
V = 366.46 (3) Å3 | T = 390 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.028 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 3.6° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
5088 measured reflections | k = −10→9 |
428 independent reflections | l = −33→17 |
428 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.014 | w = 1/[σ2(Fo2) + (0.0092P)2 + 0.9072P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.030 | (Δ/σ)max < 0.001 |
S = 1.14 | Δρmax = 1.12 e Å−3 |
428 reflections | Δρmin = −0.61 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01363 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01081 (14) | |
O3 | 0.85369 (12) | 0.7074 (2) | 0.25776 (7) | 0.0272 (2) | |
C4 | 0.0000 | 0.0000 | 0.26060 (10) | 0.0112 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01199 (5) | 0.01199 (5) | 0.01689 (7) | 0.00600 (2) | 0.000 | 0.000 |
Mg2 | 0.0093 (2) | 0.0093 (2) | 0.0138 (3) | 0.00466 (10) | 0.000 | 0.000 |
O3 | 0.0361 (5) | 0.0102 (3) | 0.0267 (4) | 0.00512 (16) | 0.00206 (16) | 0.0041 (3) |
C4 | 0.0108 (3) | 0.0108 (3) | 0.0119 (5) | 0.00541 (17) | 0.000 | 0.000 |
Ba1—O3i | 2.9447 (6) | Mg2—O3xviii | 2.0627 (11) |
Ba1—O3ii | 2.9447 (6) | Mg2—Ba1xix | 4.0287 (1) |
Ba1—O3iii | 2.9447 (6) | Mg2—Ba1xx | 4.0287 (1) |
Ba1—O3iv | 2.9447 (6) | Mg2—Ba1xvi | 4.0287 (1) |
Ba1—O3v | 2.9448 (6) | Mg2—Ba1xxi | 4.0287 (1) |
Ba1—O3vi | 2.9448 (6) | Mg2—Ba1xxii | 4.0287 (1) |
Ba1—O3vii | 2.9447 (6) | Mg2—Ba1xxiii | 4.0287 (1) |
Ba1—O3viii | 2.9447 (6) | O3—C4xxiv | 1.2732 (11) |
Ba1—O3ix | 2.9448 (6) | O3—Mg2xxv | 2.0627 (11) |
Ba1—O3x | 2.9448 (6) | O3—Ba1xix | 2.9447 (6) |
Ba1—O3xi | 2.9448 (6) | O3—Ba1xxvi | 2.9448 (6) |
Ba1—O3xii | 2.9448 (6) | C4—O3xxvii | 1.2732 (11) |
Mg2—O3xiii | 2.0627 (11) | C4—O3xxviii | 1.2732 (11) |
Mg2—O3xiv | 2.0627 (11) | C4—O3xxix | 1.2732 (11) |
Mg2—O3xv | 2.0627 (11) | C4—Ba1xvi | 3.2998 (8) |
Mg2—O3xvi | 2.0627 (11) | C4—Ba1xix | 3.2998 (8) |
Mg2—O3xvii | 2.0627 (11) | C4—Ba1xxii | 3.2998 (8) |
O3i—Ba1—O3ii | 180.00 (4) | O3xiv—Mg2—O3xviii | 86.13 (5) |
O3i—Ba1—O3iii | 57.15 (4) | O3xv—Mg2—O3xviii | 93.87 (5) |
O3ii—Ba1—O3iii | 122.85 (4) | O3xvi—Mg2—O3xviii | 86.13 (5) |
O3i—Ba1—O3iv | 122.85 (4) | O3xvii—Mg2—O3xviii | 180.00 (5) |
O3ii—Ba1—O3iv | 57.15 (4) | O3xiii—Mg2—Ba1xix | 44.697 (16) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.303 (16) |
O3i—Ba1—O3v | 43.95 (4) | O3xv—Mg2—Ba1xix | 98.05 (3) |
O3ii—Ba1—O3v | 136.05 (4) | O3xvi—Mg2—Ba1xix | 81.95 (3) |
O3iii—Ba1—O3v | 95.48 (3) | O3xvii—Mg2—Ba1xix | 44.699 (15) |
O3iv—Ba1—O3v | 84.52 (3) | O3xviii—Mg2—Ba1xix | 135.301 (15) |
O3i—Ba1—O3vi | 136.05 (4) | O3xiii—Mg2—Ba1xx | 135.303 (16) |
O3ii—Ba1—O3vi | 43.95 (4) | O3xiv—Mg2—Ba1xx | 44.697 (16) |
O3iii—Ba1—O3vi | 84.52 (3) | O3xv—Mg2—Ba1xx | 81.95 (3) |
O3iv—Ba1—O3vi | 95.48 (3) | O3xvi—Mg2—Ba1xx | 98.05 (3) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 135.301 (15) |
O3i—Ba1—O3vii | 95.48 (3) | O3xviii—Mg2—Ba1xx | 44.699 (15) |
O3ii—Ba1—O3vii | 84.52 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.95 (4) | O3xiii—Mg2—Ba1xvi | 98.05 (3) |
O3iv—Ba1—O3vii | 136.05 (4) | O3xiv—Mg2—Ba1xvi | 81.95 (3) |
O3v—Ba1—O3vii | 116.96 (4) | O3xv—Mg2—Ba1xvi | 44.697 (16) |
O3vi—Ba1—O3vii | 63.04 (4) | O3xvi—Mg2—Ba1xvi | 135.303 (16) |
O3i—Ba1—O3viii | 84.52 (3) | O3xvii—Mg2—Ba1xvi | 44.699 (16) |
O3ii—Ba1—O3viii | 95.48 (3) | O3xviii—Mg2—Ba1xvi | 135.301 (16) |
O3iii—Ba1—O3viii | 136.05 (4) | Ba1xix—Mg2—Ba1xvi | 77.087 (2) |
O3iv—Ba1—O3viii | 43.95 (4) | Ba1xx—Mg2—Ba1xvi | 102.913 (2) |
O3v—Ba1—O3viii | 63.04 (4) | O3xiii—Mg2—Ba1xxi | 81.95 (3) |
O3vi—Ba1—O3viii | 116.96 (4) | O3xiv—Mg2—Ba1xxi | 98.05 (3) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xxi | 135.303 (16) |
O3i—Ba1—O3ix | 95.48 (3) | O3xvi—Mg2—Ba1xxi | 44.697 (16) |
O3ii—Ba1—O3ix | 84.52 (3) | O3xvii—Mg2—Ba1xxi | 135.301 (16) |
O3iii—Ba1—O3ix | 116.96 (4) | O3xviii—Mg2—Ba1xxi | 44.699 (16) |
O3iv—Ba1—O3ix | 63.04 (4) | Ba1xix—Mg2—Ba1xxi | 102.913 (2) |
O3v—Ba1—O3ix | 57.15 (4) | Ba1xx—Mg2—Ba1xxi | 77.087 (2) |
O3vi—Ba1—O3ix | 122.85 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 95.48 (3) | O3xiii—Mg2—Ba1xxii | 44.699 (15) |
O3viii—Ba1—O3ix | 84.52 (3) | O3xiv—Mg2—Ba1xxii | 135.301 (15) |
O3i—Ba1—O3x | 84.52 (3) | O3xv—Mg2—Ba1xxii | 44.699 (15) |
O3ii—Ba1—O3x | 95.48 (3) | O3xvi—Mg2—Ba1xxii | 135.301 (15) |
O3iii—Ba1—O3x | 63.04 (4) | O3xvii—Mg2—Ba1xxii | 98.06 (3) |
O3iv—Ba1—O3x | 116.96 (4) | O3xviii—Mg2—Ba1xxii | 81.94 (3) |
O3v—Ba1—O3x | 122.85 (4) | Ba1xix—Mg2—Ba1xxii | 77.087 (2) |
O3vi—Ba1—O3x | 57.15 (4) | Ba1xx—Mg2—Ba1xxii | 102.913 (2) |
O3vii—Ba1—O3x | 84.52 (3) | Ba1xvi—Mg2—Ba1xxii | 77.087 (2) |
O3viii—Ba1—O3x | 95.48 (3) | Ba1xxi—Mg2—Ba1xxii | 102.913 (2) |
O3ix—Ba1—O3x | 180.00 (4) | O3xiii—Mg2—Ba1xxiii | 135.301 (15) |
O3i—Ba1—O3xi | 63.04 (4) | O3xiv—Mg2—Ba1xxiii | 44.699 (15) |
O3ii—Ba1—O3xi | 116.96 (4) | O3xv—Mg2—Ba1xxiii | 135.301 (15) |
O3iii—Ba1—O3xi | 84.52 (3) | O3xvi—Mg2—Ba1xxiii | 44.699 (15) |
O3iv—Ba1—O3xi | 95.48 (3) | O3xvii—Mg2—Ba1xxiii | 81.94 (3) |
O3v—Ba1—O3xi | 84.52 (3) | O3xviii—Mg2—Ba1xxiii | 98.06 (3) |
O3vi—Ba1—O3xi | 95.48 (3) | Ba1xix—Mg2—Ba1xxiii | 102.913 (2) |
O3vii—Ba1—O3xi | 122.85 (4) | Ba1xx—Mg2—Ba1xxiii | 77.087 (2) |
O3viii—Ba1—O3xi | 57.15 (4) | Ba1xvi—Mg2—Ba1xxiii | 102.913 (2) |
O3ix—Ba1—O3xi | 136.05 (4) | Ba1xxi—Mg2—Ba1xxiii | 77.087 (2) |
O3x—Ba1—O3xi | 43.95 (4) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.96 (4) | C4xxiv—O3—Mg2xxv | 139.90 (11) |
O3ii—Ba1—O3xii | 63.04 (4) | C4xxiv—O3—Ba1xix | 94.56 (5) |
O3iii—Ba1—O3xii | 95.48 (3) | Mg2xxv—O3—Ba1xix | 105.78 (3) |
O3iv—Ba1—O3xii | 84.52 (3) | C4xxiv—O3—Ba1xxvi | 94.56 (5) |
O3v—Ba1—O3xii | 95.48 (3) | Mg2xxv—O3—Ba1xxvi | 105.78 (3) |
O3vi—Ba1—O3xii | 84.52 (3) | Ba1xix—O3—Ba1xxvi | 116.96 (4) |
O3vii—Ba1—O3xii | 57.15 (4) | O3xxvii—C4—O3xxviii | 119.861 (13) |
O3viii—Ba1—O3xii | 122.85 (4) | O3xxvii—C4—O3xxix | 119.861 (13) |
O3ix—Ba1—O3xii | 43.95 (4) | O3xxviii—C4—O3xxix | 119.861 (13) |
O3x—Ba1—O3xii | 136.05 (4) | O3xxvii—C4—Ba1xvi | 62.82 (4) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xvi | 149.31 (12) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxix—C4—Ba1xvi | 62.82 (4) |
O3xiii—Mg2—O3xv | 86.13 (5) | O3xxvii—C4—Ba1xix | 149.31 (12) |
O3xiv—Mg2—O3xv | 93.87 (5) | O3xxviii—C4—Ba1xix | 62.82 (4) |
O3xiii—Mg2—O3xvi | 93.87 (5) | O3xxix—C4—Ba1xix | 62.82 (4) |
O3xiv—Mg2—O3xvi | 86.13 (5) | Ba1xvi—C4—Ba1xix | 99.06 (3) |
O3xv—Mg2—O3xvi | 180.00 (7) | O3xxvii—C4—Ba1xxii | 62.82 (4) |
O3xiii—Mg2—O3xvii | 86.13 (5) | O3xxviii—C4—Ba1xxii | 62.82 (4) |
O3xiv—Mg2—O3xvii | 93.87 (5) | O3xxix—C4—Ba1xxii | 149.31 (12) |
O3xv—Mg2—O3xvii | 86.13 (5) | Ba1xvi—C4—Ba1xxii | 99.06 (3) |
O3xvi—Mg2—O3xvii | 93.87 (5) | Ba1xix—C4—Ba1xxii | 99.06 (3) |
O3xiii—Mg2—O3xviii | 93.87 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.824 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 5074 reflections |
a = 5.0217 (2) Å | θ = 1.5–45° |
c = 16.8037 (6) Å | µ = 8.20 mm−1 |
V = 366.98 (3) Å3 | T = 399 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 3.6° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
5074 measured reflections | k = −10→9 |
429 independent reflections | l = −33→17 |
429 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.014 | w = 1/[σ2(Fo2) + (0.0116P)2 + 0.924P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.032 | (Δ/σ)max < 0.001 |
S = 1.12 | Δρmax = 1.27 e Å−3 |
429 reflections | Δρmin = −0.68 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01395 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01121 (15) | |
O3 | 0.85358 (13) | 0.7072 (3) | 0.25775 (7) | 0.0277 (2) | |
C4 | 0.0000 | 0.0000 | 0.26075 (11) | 0.0113 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01227 (5) | 0.01227 (5) | 0.01733 (7) | 0.00613 (2) | 0.000 | 0.000 |
Mg2 | 0.0096 (2) | 0.0096 (2) | 0.0145 (4) | 0.00479 (11) | 0.000 | 0.000 |
O3 | 0.0367 (5) | 0.0104 (3) | 0.0271 (4) | 0.00521 (17) | 0.00210 (16) | 0.0042 (3) |
C4 | 0.0109 (3) | 0.0109 (3) | 0.0123 (5) | 0.00543 (17) | 0.000 | 0.000 |
Ba1—O3i | 2.9458 (7) | Mg2—O3xviii | 2.0631 (11) |
Ba1—O3ii | 2.9458 (7) | Mg2—Ba1xix | 4.0310 (1) |
Ba1—O3iii | 2.9458 (7) | Mg2—Ba1xx | 4.0310 (1) |
Ba1—O3iv | 2.9458 (7) | Mg2—Ba1xxi | 4.0310 (1) |
Ba1—O3v | 2.9458 (7) | Mg2—Ba1xviii | 4.0310 (1) |
Ba1—O3vi | 2.9458 (7) | Mg2—Ba1xxii | 4.0310 (1) |
Ba1—O3vii | 2.9458 (7) | Mg2—Ba1xxiii | 4.0310 (1) |
Ba1—O3viii | 2.9458 (7) | O3—C4xxiv | 1.2745 (11) |
Ba1—O3ix | 2.9458 (7) | O3—Mg2xxv | 2.0631 (11) |
Ba1—O3x | 2.9458 (7) | O3—Ba1xx | 2.9458 (7) |
Ba1—O3xi | 2.9458 (7) | O3—Ba1xxvi | 2.9458 (7) |
Ba1—O3xii | 2.9458 (7) | C4—O3xxvii | 1.2745 (11) |
Mg2—O3xiii | 2.0631 (11) | C4—O3xxviii | 1.2745 (11) |
Mg2—O3xiv | 2.0631 (11) | C4—O3xxix | 1.2746 (11) |
Mg2—O3xv | 2.0631 (11) | C4—Ba1xviii | 3.3023 (9) |
Mg2—O3xvi | 2.0631 (11) | C4—Ba1xx | 3.3023 (9) |
Mg2—O3xvii | 2.0631 (11) | C4—Ba1xxiii | 3.3023 (9) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.07 (5) |
O3i—Ba1—O3iii | 57.10 (4) | O3xv—Mg2—O3xviii | 93.93 (5) |
O3ii—Ba1—O3iii | 122.90 (4) | O3xvi—Mg2—O3xviii | 86.07 (5) |
O3i—Ba1—O3iv | 122.90 (4) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 57.10 (4) | O3xiii—Mg2—Ba1xix | 135.327 (16) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 44.673 (16) |
O3i—Ba1—O3v | 43.98 (4) | O3xv—Mg2—Ba1xix | 135.327 (16) |
O3ii—Ba1—O3v | 136.02 (4) | O3xvi—Mg2—Ba1xix | 44.673 (16) |
O3iii—Ba1—O3v | 95.46 (3) | O3xvii—Mg2—Ba1xix | 82.01 (4) |
O3iv—Ba1—O3v | 84.54 (3) | O3xviii—Mg2—Ba1xix | 97.99 (4) |
O3i—Ba1—O3vi | 136.02 (4) | O3xiii—Mg2—Ba1xx | 44.673 (16) |
O3ii—Ba1—O3vi | 43.98 (4) | O3xiv—Mg2—Ba1xx | 135.327 (16) |
O3iii—Ba1—O3vi | 84.54 (3) | O3xv—Mg2—Ba1xx | 44.673 (16) |
O3iv—Ba1—O3vi | 95.46 (3) | O3xvi—Mg2—Ba1xx | 135.327 (16) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 97.99 (4) |
O3i—Ba1—O3vii | 95.46 (3) | O3xviii—Mg2—Ba1xx | 82.01 (4) |
O3ii—Ba1—O3vii | 84.54 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.98 (4) | O3xiii—Mg2—Ba1xxi | 82.01 (4) |
O3iv—Ba1—O3vii | 136.02 (4) | O3xiv—Mg2—Ba1xxi | 97.99 (4) |
O3v—Ba1—O3vii | 116.94 (4) | O3xv—Mg2—Ba1xxi | 135.327 (16) |
O3vi—Ba1—O3vii | 63.06 (4) | O3xvi—Mg2—Ba1xxi | 44.673 (16) |
O3i—Ba1—O3viii | 84.54 (3) | O3xvii—Mg2—Ba1xxi | 135.327 (16) |
O3ii—Ba1—O3viii | 95.46 (3) | O3xviii—Mg2—Ba1xxi | 44.673 (16) |
O3iii—Ba1—O3viii | 136.02 (4) | Ba1xix—Mg2—Ba1xxi | 77.054 (2) |
O3iv—Ba1—O3viii | 43.98 (4) | Ba1xx—Mg2—Ba1xxi | 102.946 (2) |
O3v—Ba1—O3viii | 63.06 (4) | O3xiii—Mg2—Ba1xviii | 97.99 (4) |
O3vi—Ba1—O3viii | 116.94 (4) | O3xiv—Mg2—Ba1xviii | 82.01 (4) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xviii | 44.673 (16) |
O3i—Ba1—O3ix | 95.46 (3) | O3xvi—Mg2—Ba1xviii | 135.327 (16) |
O3ii—Ba1—O3ix | 84.54 (3) | O3xvii—Mg2—Ba1xviii | 44.673 (16) |
O3iii—Ba1—O3ix | 116.94 (4) | O3xviii—Mg2—Ba1xviii | 135.327 (16) |
O3iv—Ba1—O3ix | 63.06 (4) | Ba1xix—Mg2—Ba1xviii | 102.946 (2) |
O3v—Ba1—O3ix | 57.10 (4) | Ba1xx—Mg2—Ba1xviii | 77.054 (2) |
O3vi—Ba1—O3ix | 122.90 (4) | Ba1xxi—Mg2—Ba1xviii | 180.0 |
O3vii—Ba1—O3ix | 95.46 (3) | O3xiii—Mg2—Ba1xxii | 135.327 (16) |
O3viii—Ba1—O3ix | 84.54 (3) | O3xiv—Mg2—Ba1xxii | 44.673 (16) |
O3i—Ba1—O3x | 84.54 (3) | O3xv—Mg2—Ba1xxii | 82.01 (3) |
O3ii—Ba1—O3x | 95.46 (3) | O3xvi—Mg2—Ba1xxii | 97.99 (3) |
O3iii—Ba1—O3x | 63.06 (4) | O3xvii—Mg2—Ba1xxii | 135.327 (16) |
O3iv—Ba1—O3x | 116.94 (4) | O3xviii—Mg2—Ba1xxii | 44.673 (16) |
O3v—Ba1—O3x | 122.90 (4) | Ba1xix—Mg2—Ba1xxii | 77.054 (2) |
O3vi—Ba1—O3x | 57.10 (4) | Ba1xx—Mg2—Ba1xxii | 102.946 (2) |
O3vii—Ba1—O3x | 84.54 (3) | Ba1xxi—Mg2—Ba1xxii | 77.054 (2) |
O3viii—Ba1—O3x | 95.46 (3) | Ba1xviii—Mg2—Ba1xxii | 102.946 (2) |
O3ix—Ba1—O3x | 180.00 (4) | O3xiii—Mg2—Ba1xxiii | 44.673 (16) |
O3i—Ba1—O3xi | 63.06 (4) | O3xiv—Mg2—Ba1xxiii | 135.327 (16) |
O3ii—Ba1—O3xi | 116.94 (4) | O3xv—Mg2—Ba1xxiii | 97.99 (3) |
O3iii—Ba1—O3xi | 84.54 (3) | O3xvi—Mg2—Ba1xxiii | 82.01 (3) |
O3iv—Ba1—O3xi | 95.46 (3) | O3xvii—Mg2—Ba1xxiii | 44.673 (16) |
O3v—Ba1—O3xi | 84.54 (3) | O3xviii—Mg2—Ba1xxiii | 135.327 (16) |
O3vi—Ba1—O3xi | 95.46 (3) | Ba1xix—Mg2—Ba1xxiii | 102.946 (2) |
O3vii—Ba1—O3xi | 122.90 (4) | Ba1xx—Mg2—Ba1xxiii | 77.054 (2) |
O3viii—Ba1—O3xi | 57.10 (4) | Ba1xxi—Mg2—Ba1xxiii | 102.946 (2) |
O3ix—Ba1—O3xi | 136.03 (4) | Ba1xviii—Mg2—Ba1xxiii | 77.054 (2) |
O3x—Ba1—O3xi | 43.97 (4) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.94 (4) | C4xxiv—O3—Mg2xxv | 139.73 (12) |
O3ii—Ba1—O3xii | 63.06 (4) | C4xxiv—O3—Ba1xx | 94.61 (5) |
O3iii—Ba1—O3xii | 95.46 (3) | Mg2xxv—O3—Ba1xx | 105.83 (3) |
O3iv—Ba1—O3xii | 84.54 (3) | C4xxiv—O3—Ba1xxvi | 94.61 (5) |
O3v—Ba1—O3xii | 95.46 (3) | Mg2xxv—O3—Ba1xxvi | 105.83 (3) |
O3vi—Ba1—O3xii | 84.54 (3) | Ba1xx—O3—Ba1xxvi | 116.94 (4) |
O3vii—Ba1—O3xii | 57.10 (4) | O3xxvii—C4—O3xxviii | 119.846 (14) |
O3viii—Ba1—O3xii | 122.90 (4) | O3xxvii—C4—O3xxix | 119.844 (14) |
O3ix—Ba1—O3xii | 43.97 (4) | O3xxviii—C4—O3xxix | 119.844 (14) |
O3x—Ba1—O3xii | 136.03 (5) | O3xxvii—C4—Ba1xviii | 62.77 (5) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xviii | 149.13 (12) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxix—C4—Ba1xviii | 62.77 (5) |
O3xiii—Mg2—O3xv | 86.07 (5) | O3xxvii—C4—Ba1xx | 149.13 (12) |
O3xiv—Mg2—O3xv | 93.93 (5) | O3xxviii—C4—Ba1xx | 62.77 (5) |
O3xiii—Mg2—O3xvi | 93.93 (5) | O3xxix—C4—Ba1xx | 62.77 (5) |
O3xiv—Mg2—O3xvi | 86.07 (5) | Ba1xviii—C4—Ba1xx | 98.99 (3) |
O3xv—Mg2—O3xvi | 180.00 (6) | O3xxvii—C4—Ba1xxiii | 62.77 (5) |
O3xiii—Mg2—O3xvii | 86.07 (5) | O3xxviii—C4—Ba1xxiii | 62.77 (5) |
O3xiv—Mg2—O3xvii | 93.93 (5) | O3xxix—C4—Ba1xxiii | 149.13 (12) |
O3xv—Mg2—O3xvii | 86.07 (5) | Ba1xviii—C4—Ba1xxiii | 98.99 (3) |
O3xvi—Mg2—O3xvii | 93.93 (5) | Ba1xx—C4—Ba1xxiii | 98.99 (3) |
O3xiii—Mg2—O3xviii | 93.93 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) x−y−1/3, x−2/3, −z+1/3; (xvi) −x+y+1/3, −x+2/3, z−1/3; (xvii) −x+2/3, −y+1/3, −z+1/3; (xviii) x−2/3, y−1/3, z−1/3; (xix) x−1/3, y−2/3, z−2/3; (xx) x+1/3, y+2/3, z−1/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x−1/3, y+1/3, z−2/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.818 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 5148 reflections |
a = 5.0224 (2) Å | θ = 1.5–45° |
c = 16.8222 (8) Å | µ = 8.19 mm−1 |
V = 367.48 (3) Å3 | T = 420 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 3.6° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
5148 measured reflections | k = −10→9 |
428 independent reflections | l = −33→17 |
428 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.013 | w = 1/[σ2(Fo2) + (0.0095P)2 + 0.744P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.031 | (Δ/σ)max < 0.001 |
S = 1.18 | Δρmax = 1.05 e Å−3 |
428 reflections | Δρmin = −0.72 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01455 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01152 (14) | |
O3 | 0.85374 (12) | 0.7075 (2) | 0.25774 (7) | 0.0283 (2) | |
C4 | 0.0000 | 0.0000 | 0.26077 (10) | 0.0119 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01277 (5) | 0.01277 (5) | 0.01812 (7) | 0.00638 (2) | 0.000 | 0.000 |
Mg2 | 0.0098 (2) | 0.0098 (2) | 0.0149 (4) | 0.00492 (10) | 0.000 | 0.000 |
O3 | 0.0370 (5) | 0.0110 (3) | 0.0284 (4) | 0.00550 (16) | 0.00219 (16) | 0.0044 (3) |
C4 | 0.0116 (3) | 0.0116 (3) | 0.0126 (5) | 0.00580 (17) | 0.000 | 0.000 |
Ba1—O3i | 2.9470 (6) | Mg2—O3xviii | 2.0653 (11) |
Ba1—O3ii | 2.9470 (6) | Mg2—Ba1xix | 4.0334 (1) |
Ba1—O3iii | 2.9470 (6) | Mg2—Ba1xx | 4.0334 (1) |
Ba1—O3iv | 2.9470 (6) | Mg2—Ba1xvi | 4.0334 (1) |
Ba1—O3v | 2.9471 (6) | Mg2—Ba1xxi | 4.0334 (1) |
Ba1—O3vi | 2.9471 (6) | Mg2—Ba1xxii | 4.0335 (1) |
Ba1—O3vii | 2.9471 (6) | Mg2—Ba1xxiii | 4.0335 (1) |
Ba1—O3viii | 2.9471 (6) | O3—C4xxiv | 1.2733 (11) |
Ba1—O3ix | 2.9471 (6) | O3—Mg2xxv | 2.0653 (11) |
Ba1—O3x | 2.9471 (6) | O3—Ba1xix | 2.9470 (6) |
Ba1—O3xi | 2.9471 (6) | O3—Ba1xxvi | 2.9471 (6) |
Ba1—O3xii | 2.9471 (6) | C4—O3xxvii | 1.2733 (11) |
Mg2—O3xiii | 2.0653 (11) | C4—O3xxviii | 1.2733 (11) |
Mg2—O3xiv | 2.0653 (11) | C4—O3xxix | 1.2733 (11) |
Mg2—O3xv | 2.0653 (11) | C4—Ba1xvi | 3.3037 (8) |
Mg2—O3xvi | 2.0653 (11) | C4—Ba1xix | 3.3037 (8) |
Mg2—O3xvii | 2.0653 (11) | C4—Ba1xxii | 3.3037 (8) |
O3i—Ba1—O3ii | 180.00 (4) | O3xiv—Mg2—O3xviii | 86.06 (5) |
O3i—Ba1—O3iii | 57.14 (4) | O3xv—Mg2—O3xviii | 93.94 (5) |
O3ii—Ba1—O3iii | 122.86 (4) | O3xvi—Mg2—O3xviii | 86.06 (5) |
O3i—Ba1—O3iv | 122.86 (4) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 57.14 (4) | O3xiii—Mg2—Ba1xix | 44.665 (16) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.335 (16) |
O3i—Ba1—O3v | 43.91 (4) | O3xv—Mg2—Ba1xix | 97.96 (3) |
O3ii—Ba1—O3v | 136.09 (4) | O3xvi—Mg2—Ba1xix | 82.04 (3) |
O3iii—Ba1—O3v | 95.43 (3) | O3xvii—Mg2—Ba1xix | 44.666 (16) |
O3iv—Ba1—O3v | 84.57 (3) | O3xviii—Mg2—Ba1xix | 135.334 (16) |
O3i—Ba1—O3vi | 136.09 (4) | O3xiii—Mg2—Ba1xx | 135.335 (16) |
O3ii—Ba1—O3vi | 43.91 (4) | O3xiv—Mg2—Ba1xx | 44.665 (16) |
O3iii—Ba1—O3vi | 84.57 (3) | O3xv—Mg2—Ba1xx | 82.04 (3) |
O3iv—Ba1—O3vi | 95.43 (3) | O3xvi—Mg2—Ba1xx | 97.96 (3) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 135.334 (16) |
O3i—Ba1—O3vii | 95.43 (3) | O3xviii—Mg2—Ba1xx | 44.666 (16) |
O3ii—Ba1—O3vii | 84.57 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.91 (4) | O3xiii—Mg2—Ba1xvi | 97.96 (3) |
O3iv—Ba1—O3vii | 136.09 (4) | O3xiv—Mg2—Ba1xvi | 82.04 (3) |
O3v—Ba1—O3vii | 116.88 (4) | O3xv—Mg2—Ba1xvi | 44.665 (16) |
O3vi—Ba1—O3vii | 63.12 (4) | O3xvi—Mg2—Ba1xvi | 135.335 (16) |
O3i—Ba1—O3viii | 84.57 (3) | O3xvii—Mg2—Ba1xvi | 44.666 (16) |
O3ii—Ba1—O3viii | 95.43 (3) | O3xviii—Mg2—Ba1xvi | 135.334 (16) |
O3iii—Ba1—O3viii | 136.09 (4) | Ba1xix—Mg2—Ba1xvi | 77.012 (3) |
O3iv—Ba1—O3viii | 43.91 (4) | Ba1xx—Mg2—Ba1xvi | 102.988 (3) |
O3v—Ba1—O3viii | 63.12 (4) | O3xiii—Mg2—Ba1xxi | 82.04 (3) |
O3vi—Ba1—O3viii | 116.88 (4) | O3xiv—Mg2—Ba1xxi | 97.96 (3) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xxi | 135.335 (16) |
O3i—Ba1—O3ix | 95.43 (3) | O3xvi—Mg2—Ba1xxi | 44.665 (16) |
O3ii—Ba1—O3ix | 84.57 (3) | O3xvii—Mg2—Ba1xxi | 135.334 (16) |
O3iii—Ba1—O3ix | 116.88 (4) | O3xviii—Mg2—Ba1xxi | 44.666 (16) |
O3iv—Ba1—O3ix | 63.12 (4) | Ba1xix—Mg2—Ba1xxi | 102.988 (3) |
O3v—Ba1—O3ix | 57.14 (4) | Ba1xx—Mg2—Ba1xxi | 77.012 (3) |
O3vi—Ba1—O3ix | 122.86 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 95.43 (3) | O3xiii—Mg2—Ba1xxii | 44.666 (16) |
O3viii—Ba1—O3ix | 84.57 (3) | O3xiv—Mg2—Ba1xxii | 135.334 (16) |
O3i—Ba1—O3x | 84.57 (3) | O3xv—Mg2—Ba1xxii | 44.666 (16) |
O3ii—Ba1—O3x | 95.43 (3) | O3xvi—Mg2—Ba1xxii | 135.334 (16) |
O3iii—Ba1—O3x | 63.12 (4) | O3xvii—Mg2—Ba1xxii | 97.96 (3) |
O3iv—Ba1—O3x | 116.88 (4) | O3xviii—Mg2—Ba1xxii | 82.04 (3) |
O3v—Ba1—O3x | 122.86 (4) | Ba1xix—Mg2—Ba1xxii | 77.012 (2) |
O3vi—Ba1—O3x | 57.14 (4) | Ba1xx—Mg2—Ba1xxii | 102.988 (2) |
O3vii—Ba1—O3x | 84.57 (3) | Ba1xvi—Mg2—Ba1xxii | 77.012 (3) |
O3viii—Ba1—O3x | 95.43 (3) | Ba1xxi—Mg2—Ba1xxii | 102.988 (3) |
O3ix—Ba1—O3x | 180.00 (4) | O3xiii—Mg2—Ba1xxiii | 135.334 (16) |
O3i—Ba1—O3xi | 63.12 (4) | O3xiv—Mg2—Ba1xxiii | 44.666 (16) |
O3ii—Ba1—O3xi | 116.88 (4) | O3xv—Mg2—Ba1xxiii | 135.334 (16) |
O3iii—Ba1—O3xi | 84.57 (3) | O3xvi—Mg2—Ba1xxiii | 44.666 (16) |
O3iv—Ba1—O3xi | 95.43 (3) | O3xvii—Mg2—Ba1xxiii | 82.04 (3) |
O3v—Ba1—O3xi | 84.57 (3) | O3xviii—Mg2—Ba1xxiii | 97.96 (3) |
O3vi—Ba1—O3xi | 95.43 (3) | Ba1xix—Mg2—Ba1xxiii | 102.988 (2) |
O3vii—Ba1—O3xi | 122.86 (4) | Ba1xx—Mg2—Ba1xxiii | 77.012 (2) |
O3viii—Ba1—O3xi | 57.14 (4) | Ba1xvi—Mg2—Ba1xxiii | 102.988 (3) |
O3ix—Ba1—O3xi | 136.09 (4) | Ba1xxi—Mg2—Ba1xxiii | 77.012 (3) |
O3x—Ba1—O3xi | 43.91 (4) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.88 (4) | C4xxiv—O3—Mg2xxv | 139.70 (11) |
O3ii—Ba1—O3xii | 63.12 (4) | C4xxiv—O3—Ba1xix | 94.65 (5) |
O3iii—Ba1—O3xii | 95.43 (3) | Mg2xxv—O3—Ba1xix | 105.82 (3) |
O3iv—Ba1—O3xii | 84.57 (3) | C4xxiv—O3—Ba1xxvi | 94.65 (5) |
O3v—Ba1—O3xii | 95.43 (3) | Mg2xxv—O3—Ba1xxvi | 105.82 (3) |
O3vi—Ba1—O3xii | 84.57 (3) | Ba1xix—O3—Ba1xxvi | 116.88 (4) |
O3vii—Ba1—O3xii | 57.14 (4) | O3xxvii—C4—O3xxviii | 119.841 (14) |
O3viii—Ba1—O3xii | 122.86 (4) | O3xxvii—C4—O3xxix | 119.841 (14) |
O3ix—Ba1—O3xii | 43.91 (4) | O3xxviii—C4—O3xxix | 119.841 (14) |
O3x—Ba1—O3xii | 136.09 (4) | O3xxvii—C4—Ba1xvi | 62.76 (4) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xvi | 149.07 (12) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxix—C4—Ba1xvi | 62.76 (4) |
O3xiii—Mg2—O3xv | 86.06 (5) | O3xxvii—C4—Ba1xix | 149.07 (12) |
O3xiv—Mg2—O3xv | 93.94 (5) | O3xxviii—C4—Ba1xix | 62.76 (4) |
O3xiii—Mg2—O3xvi | 93.94 (5) | O3xxix—C4—Ba1xix | 62.76 (4) |
O3xiv—Mg2—O3xvi | 86.06 (5) | Ba1xvi—C4—Ba1xix | 98.95 (3) |
O3xv—Mg2—O3xvi | 180.00 (5) | O3xxvii—C4—Ba1xxii | 62.76 (4) |
O3xiii—Mg2—O3xvii | 86.06 (5) | O3xxviii—C4—Ba1xxii | 62.76 (4) |
O3xiv—Mg2—O3xvii | 93.94 (5) | O3xxix—C4—Ba1xxii | 149.07 (12) |
O3xv—Mg2—O3xvii | 86.06 (5) | Ba1xvi—C4—Ba1xxii | 98.95 (3) |
O3xvi—Mg2—O3xvii | 93.94 (5) | Ba1xix—C4—Ba1xxii | 98.95 (3) |
O3xiii—Mg2—O3xviii | 93.94 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.809 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 4994 reflections |
a = 5.0228 (7) Å | θ = 1.5–45° |
c = 16.862 (3) Å | µ = 8.17 mm−1 |
V = 368.41 (13) Å3 | T = 440 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.028 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.3°, θmin = 3.6° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
4994 measured reflections | k = −10→9 |
423 independent reflections | l = −32→17 |
423 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.014 | w = 1/[σ2(Fo2) + (0.0114P)2 + 0.7897P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.032 | (Δ/σ)max < 0.001 |
S = 1.15 | Δρmax = 1.10 e Å−3 |
423 reflections | Δρmin = −0.69 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01522 (4) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01213 (15) | |
O3 | 0.85370 (13) | 0.7074 (3) | 0.25779 (8) | 0.0293 (2) | |
C4 | 0.0000 | 0.0000 | 0.26081 (11) | 0.0123 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01340 (5) | 0.01340 (5) | 0.01886 (7) | 0.00670 (2) | 0.000 | 0.000 |
Mg2 | 0.0104 (2) | 0.0104 (2) | 0.0157 (4) | 0.00518 (11) | 0.000 | 0.000 |
O3 | 0.0380 (5) | 0.0115 (4) | 0.0296 (5) | 0.00573 (18) | 0.00234 (17) | 0.0047 (3) |
C4 | 0.0121 (4) | 0.0121 (4) | 0.0129 (6) | 0.00603 (18) | 0.000 | 0.000 |
Ba1—O3i | 2.9495 (8) | Mg2—O3xviii | 2.0665 (12) |
Ba1—O3ii | 2.9495 (8) | Mg2—Ba1xix | 4.0382 (5) |
Ba1—O3iii | 2.9495 (8) | Mg2—Ba1xx | 4.0382 (5) |
Ba1—O3iv | 2.9495 (8) | Mg2—Ba1xvi | 4.0382 (5) |
Ba1—O3v | 2.9495 (8) | Mg2—Ba1xxi | 4.0382 (5) |
Ba1—O3vi | 2.9495 (8) | Mg2—Ba1xxii | 4.0382 (5) |
Ba1—O3vii | 2.9495 (8) | Mg2—Ba1xxiii | 4.0382 (5) |
Ba1—O3viii | 2.9495 (8) | O3—C4xxiv | 1.2737 (12) |
Ba1—O3ix | 2.9495 (8) | O3—Mg2xxv | 2.0665 (12) |
Ba1—O3x | 2.9495 (8) | O3—Ba1xix | 2.9495 (8) |
Ba1—O3xi | 2.9495 (8) | O3—Ba1xxvi | 2.9495 (8) |
Ba1—O3xii | 2.9495 (8) | C4—O3xxvii | 1.2737 (12) |
Mg2—O3xiii | 2.0665 (12) | C4—O3xxviii | 1.2737 (12) |
Mg2—O3xiv | 2.0665 (12) | C4—O3xxix | 1.2737 (12) |
Mg2—O3xv | 2.0665 (12) | C4—Ba1xvi | 3.3060 (10) |
Mg2—O3xvi | 2.0665 (12) | C4—Ba1xix | 3.3060 (10) |
Mg2—O3xvii | 2.0665 (12) | C4—Ba1xxii | 3.3060 (10) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 85.99 (5) |
O3i—Ba1—O3iii | 57.08 (4) | O3xv—Mg2—O3xviii | 94.01 (5) |
O3ii—Ba1—O3iii | 122.92 (4) | O3xvi—Mg2—O3xviii | 85.99 (5) |
O3i—Ba1—O3iv | 122.92 (4) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 57.08 (4) | O3xiii—Mg2—Ba1xix | 44.625 (18) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.375 (18) |
O3i—Ba1—O3v | 43.89 (5) | O3xv—Mg2—Ba1xix | 97.84 (4) |
O3ii—Ba1—O3v | 136.11 (5) | O3xvi—Mg2—Ba1xix | 82.16 (4) |
O3iii—Ba1—O3v | 95.33 (3) | O3xvii—Mg2—Ba1xix | 44.626 (17) |
O3iv—Ba1—O3v | 84.67 (3) | O3xviii—Mg2—Ba1xix | 135.374 (17) |
O3i—Ba1—O3vi | 136.11 (5) | O3xiii—Mg2—Ba1xx | 135.375 (18) |
O3ii—Ba1—O3vi | 43.89 (5) | O3xiv—Mg2—Ba1xx | 44.625 (18) |
O3iii—Ba1—O3vi | 84.67 (3) | O3xv—Mg2—Ba1xx | 82.16 (4) |
O3iv—Ba1—O3vi | 95.33 (3) | O3xvi—Mg2—Ba1xx | 97.84 (4) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 135.374 (17) |
O3i—Ba1—O3vii | 95.33 (3) | O3xviii—Mg2—Ba1xx | 44.626 (17) |
O3ii—Ba1—O3vii | 84.67 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.89 (5) | O3xiii—Mg2—Ba1xvi | 97.84 (4) |
O3iv—Ba1—O3vii | 136.11 (5) | O3xiv—Mg2—Ba1xvi | 82.16 (4) |
O3v—Ba1—O3vii | 116.74 (4) | O3xv—Mg2—Ba1xvi | 44.625 (18) |
O3vi—Ba1—O3vii | 63.26 (4) | O3xvi—Mg2—Ba1xvi | 135.375 (17) |
O3i—Ba1—O3viii | 84.67 (3) | O3xvii—Mg2—Ba1xvi | 44.626 (17) |
O3ii—Ba1—O3viii | 95.33 (3) | O3xviii—Mg2—Ba1xvi | 135.374 (17) |
O3iii—Ba1—O3viii | 136.11 (5) | Ba1xix—Mg2—Ba1xvi | 76.911 (11) |
O3iv—Ba1—O3viii | 43.89 (5) | Ba1xx—Mg2—Ba1xvi | 103.089 (11) |
O3v—Ba1—O3viii | 63.26 (4) | O3xiii—Mg2—Ba1xxi | 82.16 (4) |
O3vi—Ba1—O3viii | 116.74 (4) | O3xiv—Mg2—Ba1xxi | 97.84 (4) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xxi | 135.375 (17) |
O3i—Ba1—O3ix | 95.33 (3) | O3xvi—Mg2—Ba1xxi | 44.625 (18) |
O3ii—Ba1—O3ix | 84.67 (3) | O3xvii—Mg2—Ba1xxi | 135.374 (17) |
O3iii—Ba1—O3ix | 116.74 (4) | O3xviii—Mg2—Ba1xxi | 44.626 (17) |
O3iv—Ba1—O3ix | 63.26 (4) | Ba1xix—Mg2—Ba1xxi | 103.089 (11) |
O3v—Ba1—O3ix | 57.08 (4) | Ba1xx—Mg2—Ba1xxi | 76.911 (11) |
O3vi—Ba1—O3ix | 122.92 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 95.33 (3) | O3xiii—Mg2—Ba1xxii | 44.626 (17) |
O3viii—Ba1—O3ix | 84.67 (3) | O3xiv—Mg2—Ba1xxii | 135.374 (17) |
O3i—Ba1—O3x | 84.67 (3) | O3xv—Mg2—Ba1xxii | 44.626 (17) |
O3ii—Ba1—O3x | 95.33 (3) | O3xvi—Mg2—Ba1xxii | 135.374 (17) |
O3iii—Ba1—O3x | 63.26 (4) | O3xvii—Mg2—Ba1xxii | 97.84 (4) |
O3iv—Ba1—O3x | 116.74 (4) | O3xviii—Mg2—Ba1xxii | 82.16 (4) |
O3v—Ba1—O3x | 122.92 (4) | Ba1xix—Mg2—Ba1xxii | 76.911 (11) |
O3vi—Ba1—O3x | 57.08 (4) | Ba1xx—Mg2—Ba1xxii | 103.089 (11) |
O3vii—Ba1—O3x | 84.67 (3) | Ba1xvi—Mg2—Ba1xxii | 76.911 (11) |
O3viii—Ba1—O3x | 95.33 (3) | Ba1xxi—Mg2—Ba1xxii | 103.089 (11) |
O3ix—Ba1—O3x | 180.00 (4) | O3xiii—Mg2—Ba1xxiii | 135.374 (17) |
O3i—Ba1—O3xi | 63.26 (4) | O3xiv—Mg2—Ba1xxiii | 44.626 (17) |
O3ii—Ba1—O3xi | 116.74 (4) | O3xv—Mg2—Ba1xxiii | 135.374 (17) |
O3iii—Ba1—O3xi | 84.67 (3) | O3xvi—Mg2—Ba1xxiii | 44.626 (17) |
O3iv—Ba1—O3xi | 95.33 (3) | O3xvii—Mg2—Ba1xxiii | 82.16 (4) |
O3v—Ba1—O3xi | 84.67 (3) | O3xviii—Mg2—Ba1xxiii | 97.84 (4) |
O3vi—Ba1—O3xi | 95.33 (3) | Ba1xix—Mg2—Ba1xxiii | 103.089 (11) |
O3vii—Ba1—O3xi | 122.92 (4) | Ba1xx—Mg2—Ba1xxiii | 76.911 (11) |
O3viii—Ba1—O3xi | 57.08 (4) | Ba1xvi—Mg2—Ba1xxiii | 103.089 (11) |
O3ix—Ba1—O3xi | 136.11 (5) | Ba1xxi—Mg2—Ba1xxiii | 76.911 (11) |
O3x—Ba1—O3xi | 43.89 (5) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 116.74 (4) | C4xxiv—O3—Mg2xxv | 139.65 (12) |
O3ii—Ba1—O3xii | 63.26 (4) | C4xxiv—O3—Ba1xix | 94.64 (6) |
O3iii—Ba1—O3xii | 95.33 (3) | Mg2xxv—O3—Ba1xix | 105.89 (3) |
O3iv—Ba1—O3xii | 84.67 (3) | C4xxiv—O3—Ba1xxvi | 94.64 (6) |
O3v—Ba1—O3xii | 95.33 (3) | Mg2xxv—O3—Ba1xxvi | 105.89 (3) |
O3vi—Ba1—O3xii | 84.67 (3) | Ba1xix—O3—Ba1xxvi | 116.74 (4) |
O3vii—Ba1—O3xii | 57.08 (4) | O3xxvii—C4—O3xxviii | 119.842 (14) |
O3viii—Ba1—O3xii | 122.92 (4) | O3xxvii—C4—O3xxix | 119.842 (14) |
O3ix—Ba1—O3xii | 43.89 (5) | O3xxviii—C4—O3xxix | 119.842 (15) |
O3x—Ba1—O3xii | 136.11 (5) | O3xxvii—C4—Ba1xvi | 62.78 (5) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xvi | 149.01 (13) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxix—C4—Ba1xvi | 62.78 (5) |
O3xiii—Mg2—O3xv | 85.99 (5) | O3xxvii—C4—Ba1xix | 149.01 (13) |
O3xiv—Mg2—O3xv | 94.01 (5) | O3xxviii—C4—Ba1xix | 62.78 (5) |
O3xiii—Mg2—O3xvi | 94.01 (5) | O3xxix—C4—Ba1xix | 62.78 (5) |
O3xiv—Mg2—O3xvi | 85.99 (5) | Ba1xvi—C4—Ba1xix | 98.87 (4) |
O3xv—Mg2—O3xvi | 180.00 (6) | O3xxvii—C4—Ba1xxii | 62.78 (5) |
O3xiii—Mg2—O3xvii | 85.99 (5) | O3xxviii—C4—Ba1xxii | 62.78 (5) |
O3xiv—Mg2—O3xvii | 94.01 (5) | O3xxix—C4—Ba1xxii | 149.01 (13) |
O3xv—Mg2—O3xvii | 85.99 (5) | Ba1xvi—C4—Ba1xxii | 98.87 (4) |
O3xvi—Mg2—O3xvii | 94.01 (5) | Ba1xix—C4—Ba1xxii | 98.87 (4) |
O3xiii—Mg2—O3xviii | 94.01 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.823 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 3849 reflections |
a = 5.0256 (10) Å | θ = 1.5–45° |
c = 16.782 (6) Å | µ = 8.20 mm−1 |
V = 367.1 (2) Å3 | T = 440 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.027 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 12.5° |
Tmin = 0.7, Tmax = 0.8 | h = −9→9 |
3849 measured reflections | k = −9→10 |
413 independent reflections | l = −33→16 |
413 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.014 | w = 1/[σ2(Fo2) + (0.0178P)2 + 0.1629P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.032 | (Δ/σ)max < 0.001 |
S = 1.12 | Δρmax = 0.81 e Å−3 |
413 reflections | Δρmin = −0.76 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01569 (5) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01248 (14) | |
O3 | 0.85367 (12) | 0.7073 (2) | 0.25763 (7) | 0.0299 (2) | |
C4 | 0.0000 | 0.0000 | 0.26075 (10) | 0.0127 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01375 (5) | 0.01375 (5) | 0.01956 (7) | 0.00688 (3) | 0.000 | 0.000 |
Mg2 | 0.0106 (2) | 0.0106 (2) | 0.0163 (3) | 0.00529 (10) | 0.000 | 0.000 |
O3 | 0.0381 (5) | 0.0114 (3) | 0.0313 (4) | 0.00572 (16) | 0.00231 (16) | 0.0046 (3) |
C4 | 0.0121 (3) | 0.0121 (3) | 0.0140 (5) | 0.00606 (16) | 0.000 | 0.000 |
Ba1—O3i | 2.9454 (8) | Mg2—O3xviii | 2.0649 (11) |
Ba1—O3ii | 2.9454 (8) | Mg2—Ba1xix | 4.0301 (8) |
Ba1—O3iii | 2.9454 (8) | Mg2—Ba1xx | 4.0301 (8) |
Ba1—O3iv | 2.9454 (8) | Mg2—Ba1xxi | 4.0301 (8) |
Ba1—O3v | 2.9455 (8) | Mg2—Ba1xviii | 4.0301 (8) |
Ba1—O3vi | 2.9455 (8) | Mg2—Ba1xxii | 4.0301 (8) |
Ba1—O3vii | 2.9455 (8) | Mg2—Ba1xxiii | 4.0301 (8) |
Ba1—O3viii | 2.9455 (8) | O3—C4xxiv | 1.2748 (11) |
Ba1—O3ix | 2.9455 (8) | O3—Mg2xxv | 2.0649 (11) |
Ba1—O3x | 2.9455 (8) | O3—Ba1xx | 2.9454 (8) |
Ba1—O3xi | 2.9455 (8) | O3—Ba1xxvi | 2.9455 (8) |
Ba1—O3xii | 2.9455 (8) | C4—O3xxvii | 1.2748 (11) |
Mg2—O3xiii | 2.0649 (11) | C4—O3xxviii | 1.2748 (11) |
Mg2—O3xiv | 2.0649 (11) | C4—O3xxix | 1.2748 (11) |
Mg2—O3xv | 2.0649 (11) | C4—Ba1xviii | 3.3033 (10) |
Mg2—O3xvi | 2.0649 (11) | C4—Ba1xx | 3.3033 (10) |
Mg2—O3xvii | 2.0649 (11) | C4—Ba1xxiii | 3.3034 (10) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.11 (5) |
O3i—Ba1—O3iii | 57.19 (4) | O3xv—Mg2—O3xviii | 93.89 (5) |
O3ii—Ba1—O3iii | 122.81 (4) | O3xvi—Mg2—O3xviii | 86.11 (5) |
O3i—Ba1—O3iv | 122.81 (4) | O3xvii—Mg2—O3xviii | 180.00 (7) |
O3ii—Ba1—O3iv | 57.19 (4) | O3xiii—Mg2—Ba1xix | 135.299 (18) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 44.701 (18) |
O3i—Ba1—O3v | 43.99 (4) | O3xv—Mg2—Ba1xix | 135.299 (18) |
O3ii—Ba1—O3v | 136.01 (4) | O3xvi—Mg2—Ba1xix | 44.701 (18) |
O3iii—Ba1—O3v | 95.57 (3) | O3xvii—Mg2—Ba1xix | 81.92 (4) |
O3iv—Ba1—O3v | 84.43 (3) | O3xviii—Mg2—Ba1xix | 98.08 (4) |
O3i—Ba1—O3vi | 136.01 (4) | O3xiii—Mg2—Ba1xx | 44.701 (18) |
O3ii—Ba1—O3vi | 43.99 (4) | O3xiv—Mg2—Ba1xx | 135.299 (18) |
O3iii—Ba1—O3vi | 84.43 (3) | O3xv—Mg2—Ba1xx | 44.701 (18) |
O3iv—Ba1—O3vi | 95.57 (3) | O3xvi—Mg2—Ba1xx | 135.299 (18) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 98.08 (4) |
O3i—Ba1—O3vii | 95.57 (3) | O3xviii—Mg2—Ba1xx | 81.92 (4) |
O3ii—Ba1—O3vii | 84.43 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.99 (4) | O3xiii—Mg2—Ba1xxi | 81.92 (4) |
O3iv—Ba1—O3vii | 136.01 (4) | O3xiv—Mg2—Ba1xxi | 98.08 (4) |
O3v—Ba1—O3vii | 117.10 (5) | O3xv—Mg2—Ba1xxi | 135.299 (18) |
O3vi—Ba1—O3vii | 62.90 (5) | O3xvi—Mg2—Ba1xxi | 44.701 (18) |
O3i—Ba1—O3viii | 84.43 (3) | O3xvii—Mg2—Ba1xxi | 135.299 (18) |
O3ii—Ba1—O3viii | 95.57 (3) | O3xviii—Mg2—Ba1xxi | 44.701 (18) |
O3iii—Ba1—O3viii | 136.01 (4) | Ba1xix—Mg2—Ba1xxi | 77.146 (18) |
O3iv—Ba1—O3viii | 43.99 (4) | Ba1xx—Mg2—Ba1xxi | 102.854 (18) |
O3v—Ba1—O3viii | 62.90 (5) | O3xiii—Mg2—Ba1xviii | 98.08 (4) |
O3vi—Ba1—O3viii | 117.10 (5) | O3xiv—Mg2—Ba1xviii | 81.92 (4) |
O3vii—Ba1—O3viii | 180.00 (2) | O3xv—Mg2—Ba1xviii | 44.701 (18) |
O3i—Ba1—O3ix | 95.57 (3) | O3xvi—Mg2—Ba1xviii | 135.299 (18) |
O3ii—Ba1—O3ix | 84.43 (3) | O3xvii—Mg2—Ba1xviii | 44.701 (18) |
O3iii—Ba1—O3ix | 117.10 (5) | O3xviii—Mg2—Ba1xviii | 135.299 (18) |
O3iv—Ba1—O3ix | 62.90 (5) | Ba1xix—Mg2—Ba1xviii | 102.854 (18) |
O3v—Ba1—O3ix | 57.19 (4) | Ba1xx—Mg2—Ba1xviii | 77.146 (18) |
O3vi—Ba1—O3ix | 122.81 (4) | Ba1xxi—Mg2—Ba1xviii | 180.0 |
O3vii—Ba1—O3ix | 95.57 (3) | O3xiii—Mg2—Ba1xxii | 135.299 (18) |
O3viii—Ba1—O3ix | 84.43 (3) | O3xiv—Mg2—Ba1xxii | 44.701 (18) |
O3i—Ba1—O3x | 84.43 (3) | O3xv—Mg2—Ba1xxii | 81.92 (4) |
O3ii—Ba1—O3x | 95.57 (3) | O3xvi—Mg2—Ba1xxii | 98.08 (4) |
O3iii—Ba1—O3x | 62.90 (5) | O3xvii—Mg2—Ba1xxii | 135.299 (18) |
O3iv—Ba1—O3x | 117.10 (5) | O3xviii—Mg2—Ba1xxii | 44.701 (18) |
O3v—Ba1—O3x | 122.81 (4) | Ba1xix—Mg2—Ba1xxii | 77.146 (18) |
O3vi—Ba1—O3x | 57.19 (4) | Ba1xx—Mg2—Ba1xxii | 102.854 (19) |
O3vii—Ba1—O3x | 84.43 (3) | Ba1xxi—Mg2—Ba1xxii | 77.146 (18) |
O3viii—Ba1—O3x | 95.57 (3) | Ba1xviii—Mg2—Ba1xxii | 102.854 (18) |
O3ix—Ba1—O3x | 180.0 | O3xiii—Mg2—Ba1xxiii | 44.701 (18) |
O3i—Ba1—O3xi | 62.90 (5) | O3xiv—Mg2—Ba1xxiii | 135.299 (18) |
O3ii—Ba1—O3xi | 117.10 (5) | O3xv—Mg2—Ba1xxiii | 98.08 (4) |
O3iii—Ba1—O3xi | 84.43 (3) | O3xvi—Mg2—Ba1xxiii | 81.92 (4) |
O3iv—Ba1—O3xi | 95.57 (3) | O3xvii—Mg2—Ba1xxiii | 44.701 (18) |
O3v—Ba1—O3xi | 84.43 (3) | O3xviii—Mg2—Ba1xxiii | 135.299 (18) |
O3vi—Ba1—O3xi | 95.57 (3) | Ba1xix—Mg2—Ba1xxiii | 102.854 (19) |
O3vii—Ba1—O3xi | 122.81 (4) | Ba1xx—Mg2—Ba1xxiii | 77.146 (18) |
O3viii—Ba1—O3xi | 57.19 (4) | Ba1xxi—Mg2—Ba1xxiii | 102.854 (18) |
O3ix—Ba1—O3xi | 136.01 (4) | Ba1xviii—Mg2—Ba1xxiii | 77.146 (18) |
O3x—Ba1—O3xi | 43.99 (4) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 117.10 (5) | C4xxiv—O3—Mg2xxv | 139.67 (11) |
O3ii—Ba1—O3xii | 62.90 (5) | C4xxiv—O3—Ba1xx | 94.67 (5) |
O3iii—Ba1—O3xii | 95.57 (3) | Mg2xxv—O3—Ba1xx | 105.75 (3) |
O3iv—Ba1—O3xii | 84.43 (3) | C4xxiv—O3—Ba1xxvi | 94.67 (5) |
O3v—Ba1—O3xii | 95.57 (3) | Mg2xxv—O3—Ba1xxvi | 105.75 (3) |
O3vi—Ba1—O3xii | 84.43 (3) | Ba1xx—O3—Ba1xxvi | 117.10 (5) |
O3vii—Ba1—O3xii | 57.19 (4) | O3xxvii—C4—O3xxviii | 119.834 (14) |
O3viii—Ba1—O3xii | 122.81 (4) | O3xxvii—C4—O3xxix | 119.831 (13) |
O3ix—Ba1—O3xii | 43.99 (4) | O3xxviii—C4—O3xxix | 119.831 (14) |
O3x—Ba1—O3xii | 136.01 (4) | O3xxvii—C4—Ba1xviii | 62.71 (4) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xviii | 149.09 (11) |
O3xiii—Mg2—O3xiv | 180.00 (5) | O3xxix—C4—Ba1xviii | 62.71 (4) |
O3xiii—Mg2—O3xv | 86.11 (5) | O3xxvii—C4—Ba1xx | 149.09 (11) |
O3xiv—Mg2—O3xv | 93.89 (5) | O3xxviii—C4—Ba1xx | 62.71 (4) |
O3xiii—Mg2—O3xvi | 93.89 (5) | O3xxix—C4—Ba1xx | 62.71 (4) |
O3xiv—Mg2—O3xvi | 86.11 (5) | Ba1xviii—C4—Ba1xx | 99.05 (3) |
O3xv—Mg2—O3xvi | 180.00 (5) | O3xxvii—C4—Ba1xxiii | 62.71 (4) |
O3xiii—Mg2—O3xvii | 86.11 (5) | O3xxviii—C4—Ba1xxiii | 62.71 (4) |
O3xiv—Mg2—O3xvii | 93.89 (5) | O3xxix—C4—Ba1xxiii | 149.09 (11) |
O3xv—Mg2—O3xvii | 86.11 (5) | Ba1xviii—C4—Ba1xxiii | 99.05 (3) |
O3xvi—Mg2—O3xvii | 93.89 (5) | Ba1xx—C4—Ba1xxiii | 99.05 (3) |
O3xiii—Mg2—O3xviii | 93.89 (5) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) x−y−1/3, x−2/3, −z+1/3; (xvi) −x+y+1/3, −x+2/3, z−1/3; (xvii) −x+2/3, −y+1/3, −z+1/3; (xviii) x−2/3, y−1/3, z−1/3; (xix) x−1/3, y−2/3, z−2/3; (xx) x+1/3, y+2/3, z−1/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x−1/3, y+1/3, z−2/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.821 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 3872 reflections |
a = 5.027 (1) Å | θ = 1.5–45° |
c = 16.778 (3) Å | µ = 8.20 mm−1 |
V = 367.20 (16) Å3 | T = 480 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.029 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.6°, θmin = 12.5° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
3872 measured reflections | k = −10→10 |
415 independent reflections | l = −16→33 |
414 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.015 | w = 1/[σ2(Fo2) + (0.0175P)2 + 0.4063P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.034 | (Δ/σ)max < 0.001 |
S = 1.08 | Δρmax = 0.84 e Å−3 |
415 reflections | Δρmin = −0.78 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01625 (5) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01278 (15) | |
O3 | 0.85365 (13) | 0.7073 (3) | 0.25768 (8) | 0.0306 (2) | |
C4 | 0.0000 | 0.0000 | 0.26074 (10) | 0.0130 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01419 (5) | 0.01419 (5) | 0.02038 (7) | 0.00709 (3) | 0.000 | 0.000 |
Mg2 | 0.0108 (2) | 0.0108 (2) | 0.0167 (3) | 0.00542 (11) | 0.000 | 0.000 |
O3 | 0.0382 (5) | 0.0119 (3) | 0.0329 (5) | 0.00596 (17) | 0.00260 (17) | 0.0052 (3) |
C4 | 0.0121 (3) | 0.0121 (3) | 0.0148 (5) | 0.00607 (17) | 0.000 | 0.000 |
Ba1—O3i | 2.9463 (8) | Mg2—O3xviii | 2.0645 (12) |
Ba1—O3ii | 2.9463 (8) | Mg2—Ba1xix | 4.0303 (5) |
Ba1—O3iii | 2.9463 (8) | Mg2—Ba1xx | 4.0303 (5) |
Ba1—O3iv | 2.9463 (8) | Mg2—Ba1xvi | 4.0303 (5) |
Ba1—O3v | 2.9463 (8) | Mg2—Ba1xxi | 4.0303 (5) |
Ba1—O3vi | 2.9463 (8) | Mg2—Ba1xxii | 4.0303 (5) |
Ba1—O3vii | 2.9463 (8) | Mg2—Ba1xxiii | 4.0303 (5) |
Ba1—O3viii | 2.9463 (8) | O3—C4xxiv | 1.2753 (12) |
Ba1—O3ix | 2.9463 (8) | O3—Mg2xxv | 2.0645 (12) |
Ba1—O3x | 2.9463 (8) | O3—Ba1xix | 2.9463 (8) |
Ba1—O3xi | 2.9463 (8) | O3—Ba1xxvi | 2.9463 (8) |
Ba1—O3xii | 2.9463 (8) | C4—O3xxvii | 1.2753 (12) |
Mg2—O3xiii | 2.0645 (12) | C4—O3xxviii | 1.2753 (12) |
Mg2—O3xiv | 2.0645 (12) | C4—O3xxix | 1.2753 (12) |
Mg2—O3xv | 2.0645 (12) | C4—Ba1xvi | 3.3038 (10) |
Mg2—O3xvi | 2.0645 (12) | C4—Ba1xix | 3.3038 (10) |
Mg2—O3xvii | 2.0645 (12) | C4—Ba1xxii | 3.3038 (10) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.15 (6) |
O3i—Ba1—O3iii | 57.18 (4) | O3xv—Mg2—O3xviii | 93.85 (6) |
O3ii—Ba1—O3iii | 122.82 (4) | O3xvi—Mg2—O3xviii | 86.15 (6) |
O3i—Ba1—O3iv | 122.82 (4) | O3xvii—Mg2—O3xviii | 180.00 (6) |
O3ii—Ba1—O3iv | 57.18 (4) | O3xiii—Mg2—Ba1xix | 44.716 (18) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 135.284 (18) |
O3i—Ba1—O3v | 43.99 (5) | O3xv—Mg2—Ba1xix | 98.12 (4) |
O3ii—Ba1—O3v | 136.01 (5) | O3xvi—Mg2—Ba1xix | 81.88 (4) |
O3iii—Ba1—O3v | 95.57 (3) | O3xvii—Mg2—Ba1xix | 44.717 (18) |
O3iv—Ba1—O3v | 84.43 (3) | O3xviii—Mg2—Ba1xix | 135.283 (18) |
O3i—Ba1—O3vi | 136.01 (5) | O3xiii—Mg2—Ba1xx | 135.284 (18) |
O3ii—Ba1—O3vi | 43.99 (5) | O3xiv—Mg2—Ba1xx | 44.716 (18) |
O3iii—Ba1—O3vi | 84.43 (3) | O3xv—Mg2—Ba1xx | 81.88 (4) |
O3iv—Ba1—O3vi | 95.57 (3) | O3xvi—Mg2—Ba1xx | 98.12 (4) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 135.283 (18) |
O3i—Ba1—O3vii | 95.57 (3) | O3xviii—Mg2—Ba1xx | 44.717 (18) |
O3ii—Ba1—O3vii | 84.43 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.99 (5) | O3xiii—Mg2—Ba1xvi | 98.12 (4) |
O3iv—Ba1—O3vii | 136.01 (5) | O3xiv—Mg2—Ba1xvi | 81.88 (4) |
O3v—Ba1—O3vii | 117.10 (5) | O3xv—Mg2—Ba1xvi | 44.716 (18) |
O3vi—Ba1—O3vii | 62.90 (5) | O3xvi—Mg2—Ba1xvi | 135.284 (18) |
O3i—Ba1—O3viii | 84.43 (3) | O3xvii—Mg2—Ba1xvi | 44.718 (18) |
O3ii—Ba1—O3viii | 95.57 (3) | O3xviii—Mg2—Ba1xvi | 135.282 (18) |
O3iii—Ba1—O3viii | 136.01 (5) | Ba1xix—Mg2—Ba1xvi | 77.167 (12) |
O3iv—Ba1—O3viii | 43.99 (5) | Ba1xx—Mg2—Ba1xvi | 102.833 (12) |
O3v—Ba1—O3viii | 62.90 (5) | O3xiii—Mg2—Ba1xxi | 81.88 (4) |
O3vi—Ba1—O3viii | 117.10 (5) | O3xiv—Mg2—Ba1xxi | 98.12 (4) |
O3vii—Ba1—O3viii | 180.00 (2) | O3xv—Mg2—Ba1xxi | 135.284 (18) |
O3i—Ba1—O3ix | 95.57 (3) | O3xvi—Mg2—Ba1xxi | 44.716 (18) |
O3ii—Ba1—O3ix | 84.43 (3) | O3xvii—Mg2—Ba1xxi | 135.282 (18) |
O3iii—Ba1—O3ix | 117.10 (5) | O3xviii—Mg2—Ba1xxi | 44.718 (18) |
O3iv—Ba1—O3ix | 62.90 (5) | Ba1xix—Mg2—Ba1xxi | 102.833 (12) |
O3v—Ba1—O3ix | 57.18 (4) | Ba1xx—Mg2—Ba1xxi | 77.167 (12) |
O3vi—Ba1—O3ix | 122.82 (4) | Ba1xvi—Mg2—Ba1xxi | 180.0 |
O3vii—Ba1—O3ix | 95.57 (3) | O3xiii—Mg2—Ba1xxii | 44.718 (18) |
O3viii—Ba1—O3ix | 84.43 (3) | O3xiv—Mg2—Ba1xxii | 135.282 (18) |
O3i—Ba1—O3x | 84.43 (3) | O3xv—Mg2—Ba1xxii | 44.718 (18) |
O3ii—Ba1—O3x | 95.57 (3) | O3xvi—Mg2—Ba1xxii | 135.282 (18) |
O3iii—Ba1—O3x | 62.90 (5) | O3xvii—Mg2—Ba1xxii | 98.12 (4) |
O3iv—Ba1—O3x | 117.10 (5) | O3xviii—Mg2—Ba1xxii | 81.88 (4) |
O3v—Ba1—O3x | 122.82 (4) | Ba1xix—Mg2—Ba1xxii | 77.167 (12) |
O3vi—Ba1—O3x | 57.18 (4) | Ba1xx—Mg2—Ba1xxii | 102.833 (12) |
O3vii—Ba1—O3x | 84.43 (3) | Ba1xvi—Mg2—Ba1xxii | 77.167 (12) |
O3viii—Ba1—O3x | 95.57 (3) | Ba1xxi—Mg2—Ba1xxii | 102.833 (12) |
O3ix—Ba1—O3x | 180.0 | O3xiii—Mg2—Ba1xxiii | 135.282 (18) |
O3i—Ba1—O3xi | 62.90 (5) | O3xiv—Mg2—Ba1xxiii | 44.718 (18) |
O3ii—Ba1—O3xi | 117.10 (5) | O3xv—Mg2—Ba1xxiii | 135.282 (18) |
O3iii—Ba1—O3xi | 84.43 (3) | O3xvi—Mg2—Ba1xxiii | 44.718 (18) |
O3iv—Ba1—O3xi | 95.57 (3) | O3xvii—Mg2—Ba1xxiii | 81.88 (4) |
O3v—Ba1—O3xi | 84.43 (3) | O3xviii—Mg2—Ba1xxiii | 98.12 (4) |
O3vi—Ba1—O3xi | 95.57 (3) | Ba1xix—Mg2—Ba1xxiii | 102.833 (12) |
O3vii—Ba1—O3xi | 122.82 (4) | Ba1xx—Mg2—Ba1xxiii | 77.167 (12) |
O3viii—Ba1—O3xi | 57.18 (4) | Ba1xvi—Mg2—Ba1xxiii | 102.833 (12) |
O3ix—Ba1—O3xi | 136.01 (5) | Ba1xxi—Mg2—Ba1xxiii | 77.167 (12) |
O3x—Ba1—O3xi | 43.99 (5) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 117.10 (5) | C4xxiv—O3—Mg2xxv | 139.74 (12) |
O3ii—Ba1—O3xii | 62.90 (5) | C4xxiv—O3—Ba1xix | 94.64 (5) |
O3iii—Ba1—O3xii | 95.57 (3) | Mg2xxv—O3—Ba1xix | 105.74 (3) |
O3iv—Ba1—O3xii | 84.43 (3) | C4xxiv—O3—Ba1xxvi | 94.64 (5) |
O3v—Ba1—O3xii | 95.57 (3) | Mg2xxv—O3—Ba1xxvi | 105.74 (3) |
O3vi—Ba1—O3xii | 84.43 (3) | Ba1xix—O3—Ba1xxvi | 117.10 (5) |
O3vii—Ba1—O3xii | 57.18 (4) | O3xxvii—C4—O3xxviii | 119.838 (14) |
O3viii—Ba1—O3xii | 122.82 (4) | O3xxvii—C4—O3xxix | 119.838 (14) |
O3ix—Ba1—O3xii | 43.99 (5) | O3xxviii—C4—O3xxix | 119.838 (14) |
O3x—Ba1—O3xii | 136.01 (5) | O3xxvii—C4—Ba1xvi | 62.73 (5) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xvi | 149.15 (12) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxix—C4—Ba1xvi | 62.73 (5) |
O3xiii—Mg2—O3xv | 86.15 (6) | O3xxvii—C4—Ba1xix | 149.15 (12) |
O3xiv—Mg2—O3xv | 93.85 (6) | O3xxviii—C4—Ba1xix | 62.73 (5) |
O3xiii—Mg2—O3xvi | 93.85 (6) | O3xxix—C4—Ba1xix | 62.73 (5) |
O3xiv—Mg2—O3xvi | 86.15 (6) | Ba1xvi—C4—Ba1xix | 99.07 (4) |
O3xv—Mg2—O3xvi | 180.00 (6) | O3xxvii—C4—Ba1xxii | 62.73 (5) |
O3xiii—Mg2—O3xvii | 86.15 (6) | O3xxviii—C4—Ba1xxii | 62.73 (5) |
O3xiv—Mg2—O3xvii | 93.85 (6) | O3xxix—C4—Ba1xxii | 149.15 (12) |
O3xv—Mg2—O3xvii | 86.15 (6) | Ba1xvi—C4—Ba1xxii | 99.07 (4) |
O3xvi—Mg2—O3xvii | 93.85 (6) | Ba1xix—C4—Ba1xxii | 99.07 (3) |
O3xiii—Mg2—O3xviii | 93.85 (6) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) −x+2/3, −y+1/3, −z+1/3; (xvi) x−2/3, y−1/3, z−1/3; (xvii) x−y−1/3, x−2/3, −z+1/3; (xviii) −x+y+1/3, −x+2/3, z−1/3; (xix) x+1/3, y+2/3, z−1/3; (xx) x−1/3, y−2/3, z−2/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x+1/3, y−1/3, z−1/3; (xxiii) x−1/3, y+1/3, z−2/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |
C6Ba3Mg3O18 | Dx = 3.816 Mg m−3 |
Mr = 845.01 | Mo Kα radiation, λ = 0.71073 Å |
Trigonal, R3m | Cell parameters from 4296 reflections |
a = 5.0277 (4) Å | θ = 1.5–45° |
c = 16.7972 (14) Å | µ = 8.19 mm−1 |
V = 367.71 (7) Å3 | T = 500 K |
Z = 1 | Prismatic |
F(000) = 384 | 0.06 × 0.03 × 0.03 mm |
StoeStadiVari diffractometer | Rint = 0.033 |
Absorption correction: numerical (Stoe & Cie GmbH 2016) | θmax = 45.5°, θmin = 12.5° |
Tmin = 0.7, Tmax = 0.8 | h = −9→10 |
4296 measured reflections | k = −10→9 |
415 independent reflections | l = −33→18 |
415 reflections with I > 2σ(I) |
Refinement on F2 | 14 parameters |
Least-squares matrix: full | 0 restraints |
R[F2 > 2σ(F2)] = 0.015 | w = 1/[σ2(Fo2) + (0.018P)2 + 0.2798P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.035 | (Δ/σ)max < 0.001 |
S = 1.12 | Δρmax = 1.46 e Å−3 |
415 reflections | Δρmin = −0.81 e Å−3 |
Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes. |
x | y | z | Uiso*/Ueq | ||
Ba1 | 0.0000 | 0.0000 | 0.5000 | 0.01686 (5) | |
Mg2 | 0.0000 | 0.0000 | 0.0000 | 0.01337 (15) | |
O3 | 0.85378 (13) | 0.7076 (3) | 0.25766 (8) | 0.0314 (3) | |
C4 | 0.0000 | 0.0000 | 0.26088 (11) | 0.0133 (2) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Ba1 | 0.01471 (5) | 0.01471 (5) | 0.02116 (8) | 0.00736 (3) | 0.000 | 0.000 |
Mg2 | 0.0113 (2) | 0.0113 (2) | 0.0175 (4) | 0.00566 (11) | 0.000 | 0.000 |
O3 | 0.0397 (6) | 0.0120 (3) | 0.0335 (5) | 0.00599 (17) | 0.00250 (17) | 0.0050 (3) |
C4 | 0.0124 (3) | 0.0124 (3) | 0.0150 (6) | 0.00621 (17) | 0.000 | 0.000 |
Ba1—O3i | 2.9474 (7) | Mg2—O3xviii | 2.0666 (12) |
Ba1—O3ii | 2.9474 (7) | Mg2—Ba1xix | 4.0327 (2) |
Ba1—O3iii | 2.9474 (7) | Mg2—Ba1xx | 4.0327 (2) |
Ba1—O3iv | 2.9474 (7) | Mg2—Ba1xxi | 4.0327 (2) |
Ba1—O3v | 2.9474 (7) | Mg2—Ba1xviii | 4.0327 (2) |
Ba1—O3vi | 2.9474 (7) | Mg2—Ba1xxii | 4.0328 (2) |
Ba1—O3vii | 2.9474 (7) | Mg2—Ba1xxiii | 4.0328 (2) |
Ba1—O3viii | 2.9474 (7) | O3—C4xxiv | 1.2745 (12) |
Ba1—O3ix | 2.9475 (7) | O3—Mg2xxv | 2.0666 (12) |
Ba1—O3x | 2.9475 (7) | O3—Ba1xx | 2.9474 (7) |
Ba1—O3xi | 2.9475 (7) | O3—Ba1xxvi | 2.9475 (7) |
Ba1—O3xii | 2.9475 (7) | C4—O3xxvii | 1.2745 (12) |
Mg2—O3xiii | 2.0666 (12) | C4—O3xxviii | 1.2745 (12) |
Mg2—O3xiv | 2.0666 (12) | C4—O3xxix | 1.2745 (12) |
Mg2—O3xv | 2.0666 (12) | C4—Ba1xviii | 3.3061 (9) |
Mg2—O3xvi | 2.0666 (12) | C4—Ba1xx | 3.3061 (9) |
Mg2—O3xvii | 2.0666 (12) | C4—Ba1xxiii | 3.3061 (9) |
O3i—Ba1—O3ii | 180.0 | O3xiv—Mg2—O3xviii | 86.13 (6) |
O3i—Ba1—O3iii | 57.21 (4) | O3xv—Mg2—O3xviii | 93.87 (6) |
O3ii—Ba1—O3iii | 122.79 (5) | O3xvi—Mg2—O3xviii | 86.13 (6) |
O3i—Ba1—O3iv | 122.79 (5) | O3xvii—Mg2—O3xviii | 179.97 (2) |
O3ii—Ba1—O3iv | 57.21 (4) | O3xiii—Mg2—Ba1xix | 135.297 (18) |
O3iii—Ba1—O3iv | 180.0 | O3xiv—Mg2—Ba1xix | 44.703 (18) |
O3i—Ba1—O3v | 43.94 (5) | O3xv—Mg2—Ba1xix | 135.296 (18) |
O3ii—Ba1—O3v | 136.06 (5) | O3xvi—Mg2—Ba1xix | 44.704 (18) |
O3iii—Ba1—O3v | 95.55 (3) | O3xvii—Mg2—Ba1xix | 81.92 (4) |
O3iv—Ba1—O3v | 84.45 (3) | O3xviii—Mg2—Ba1xix | 98.08 (4) |
O3i—Ba1—O3vi | 136.06 (5) | O3xiii—Mg2—Ba1xx | 44.703 (18) |
O3ii—Ba1—O3vi | 43.94 (5) | O3xiv—Mg2—Ba1xx | 135.297 (18) |
O3iii—Ba1—O3vi | 84.45 (3) | O3xv—Mg2—Ba1xx | 44.704 (18) |
O3iv—Ba1—O3vi | 95.55 (3) | O3xvi—Mg2—Ba1xx | 135.296 (18) |
O3v—Ba1—O3vi | 180.0 | O3xvii—Mg2—Ba1xx | 98.08 (4) |
O3i—Ba1—O3vii | 95.55 (3) | O3xviii—Mg2—Ba1xx | 81.92 (4) |
O3ii—Ba1—O3vii | 84.45 (3) | Ba1xix—Mg2—Ba1xx | 180.0 |
O3iii—Ba1—O3vii | 43.94 (5) | O3xiii—Mg2—Ba1xxi | 81.92 (4) |
O3iv—Ba1—O3vii | 136.06 (5) | O3xiv—Mg2—Ba1xxi | 98.08 (4) |
O3v—Ba1—O3vii | 117.06 (5) | O3xv—Mg2—Ba1xxi | 135.296 (18) |
O3vi—Ba1—O3vii | 62.94 (5) | O3xvi—Mg2—Ba1xxi | 44.704 (18) |
O3i—Ba1—O3viii | 84.45 (3) | O3xvii—Mg2—Ba1xxi | 135.297 (18) |
O3ii—Ba1—O3viii | 95.55 (3) | O3xviii—Mg2—Ba1xxi | 44.703 (18) |
O3iii—Ba1—O3viii | 136.06 (5) | Ba1xix—Mg2—Ba1xxi | 77.124 (5) |
O3iv—Ba1—O3viii | 43.94 (5) | Ba1xx—Mg2—Ba1xxi | 102.876 (5) |
O3v—Ba1—O3viii | 62.94 (5) | O3xiii—Mg2—Ba1xviii | 98.08 (4) |
O3vi—Ba1—O3viii | 117.06 (5) | O3xiv—Mg2—Ba1xviii | 81.92 (4) |
O3vii—Ba1—O3viii | 180.0 | O3xv—Mg2—Ba1xviii | 44.704 (18) |
O3i—Ba1—O3ix | 95.54 (3) | O3xvi—Mg2—Ba1xviii | 135.296 (18) |
O3ii—Ba1—O3ix | 84.46 (3) | O3xvii—Mg2—Ba1xviii | 44.703 (18) |
O3iii—Ba1—O3ix | 117.06 (5) | O3xviii—Mg2—Ba1xviii | 135.297 (18) |
O3iv—Ba1—O3ix | 62.94 (5) | Ba1xix—Mg2—Ba1xviii | 102.876 (5) |
O3v—Ba1—O3ix | 57.21 (4) | Ba1xx—Mg2—Ba1xviii | 77.124 (5) |
O3vi—Ba1—O3ix | 122.79 (4) | Ba1xxi—Mg2—Ba1xviii | 180.0 |
O3vii—Ba1—O3ix | 95.54 (3) | O3xiii—Mg2—Ba1xxii | 135.296 (18) |
O3viii—Ba1—O3ix | 84.46 (3) | O3xiv—Mg2—Ba1xxii | 44.704 (18) |
O3i—Ba1—O3x | 84.46 (3) | O3xv—Mg2—Ba1xxii | 81.92 (4) |
O3ii—Ba1—O3x | 95.54 (3) | O3xvi—Mg2—Ba1xxii | 98.08 (4) |
O3iii—Ba1—O3x | 62.94 (5) | O3xvii—Mg2—Ba1xxii | 135.296 (18) |
O3iv—Ba1—O3x | 117.06 (5) | O3xviii—Mg2—Ba1xxii | 44.704 (18) |
O3v—Ba1—O3x | 122.79 (4) | Ba1xix—Mg2—Ba1xxii | 77.124 (5) |
O3vi—Ba1—O3x | 57.21 (4) | Ba1xx—Mg2—Ba1xxii | 102.876 (5) |
O3vii—Ba1—O3x | 84.46 (3) | Ba1xxi—Mg2—Ba1xxii | 77.124 (5) |
O3viii—Ba1—O3x | 95.54 (3) | Ba1xviii—Mg2—Ba1xxii | 102.876 (5) |
O3ix—Ba1—O3x | 180.00 (5) | O3xiii—Mg2—Ba1xxiii | 44.704 (18) |
O3i—Ba1—O3xi | 62.94 (5) | O3xiv—Mg2—Ba1xxiii | 135.296 (18) |
O3ii—Ba1—O3xi | 117.06 (5) | O3xv—Mg2—Ba1xxiii | 98.08 (4) |
O3iii—Ba1—O3xi | 84.46 (3) | O3xvi—Mg2—Ba1xxiii | 81.92 (4) |
O3iv—Ba1—O3xi | 95.54 (3) | O3xvii—Mg2—Ba1xxiii | 44.704 (18) |
O3v—Ba1—O3xi | 84.46 (3) | O3xviii—Mg2—Ba1xxiii | 135.296 (18) |
O3vi—Ba1—O3xi | 95.54 (3) | Ba1xix—Mg2—Ba1xxiii | 102.876 (5) |
O3vii—Ba1—O3xi | 122.79 (4) | Ba1xx—Mg2—Ba1xxiii | 77.124 (5) |
O3viii—Ba1—O3xi | 57.21 (4) | Ba1xxi—Mg2—Ba1xxiii | 102.876 (5) |
O3ix—Ba1—O3xi | 136.06 (5) | Ba1xviii—Mg2—Ba1xxiii | 77.124 (5) |
O3x—Ba1—O3xi | 43.94 (5) | Ba1xxii—Mg2—Ba1xxiii | 180.0 |
O3i—Ba1—O3xii | 117.06 (5) | C4xxiv—O3—Mg2xxv | 139.61 (12) |
O3ii—Ba1—O3xii | 62.94 (5) | C4xxiv—O3—Ba1xx | 94.72 (6) |
O3iii—Ba1—O3xii | 95.54 (3) | Mg2xxv—O3—Ba1xx | 105.74 (3) |
O3iv—Ba1—O3xii | 84.46 (3) | C4xxiv—O3—Ba1xxvi | 94.72 (6) |
O3v—Ba1—O3xii | 95.54 (3) | Mg2xxv—O3—Ba1xxvi | 105.74 (3) |
O3vi—Ba1—O3xii | 84.46 (3) | Ba1xx—O3—Ba1xxvi | 117.06 (5) |
O3vii—Ba1—O3xii | 57.21 (4) | O3xxvii—C4—O3xxviii | 119.823 (15) |
O3viii—Ba1—O3xii | 122.79 (4) | O3xxvii—C4—O3xxix | 119.821 (15) |
O3ix—Ba1—O3xii | 43.94 (5) | O3xxviii—C4—O3xxix | 119.821 (15) |
O3x—Ba1—O3xii | 136.06 (5) | O3xxvii—C4—Ba1xviii | 62.68 (5) |
O3xi—Ba1—O3xii | 180.0 | O3xxviii—C4—Ba1xviii | 148.97 (12) |
O3xiii—Mg2—O3xiv | 180.00 (6) | O3xxix—C4—Ba1xviii | 62.68 (5) |
O3xiii—Mg2—O3xv | 86.13 (6) | O3xxvii—C4—Ba1xx | 148.97 (12) |
O3xiv—Mg2—O3xv | 93.87 (6) | O3xxviii—C4—Ba1xx | 62.68 (5) |
O3xiii—Mg2—O3xvi | 93.87 (6) | O3xxix—C4—Ba1xx | 62.68 (5) |
O3xiv—Mg2—O3xvi | 86.13 (6) | Ba1xviii—C4—Ba1xx | 98.99 (4) |
O3xv—Mg2—O3xvi | 180.00 (6) | O3xxvii—C4—Ba1xxiii | 62.68 (5) |
O3xiii—Mg2—O3xvii | 86.13 (6) | O3xxviii—C4—Ba1xxiii | 62.68 (5) |
O3xiv—Mg2—O3xvii | 93.87 (6) | O3xxix—C4—Ba1xxiii | 148.97 (12) |
O3xv—Mg2—O3xvii | 86.13 (6) | Ba1xviii—C4—Ba1xxiii | 98.99 (4) |
O3xvi—Mg2—O3xvii | 93.87 (6) | Ba1xx—C4—Ba1xxiii | 98.99 (4) |
O3xiii—Mg2—O3xviii | 93.87 (6) |
Symmetry codes: (i) −x+1/3, −y+2/3, −z+2/3; (ii) x−1/3, y−2/3, z+1/3; (iii) y−2/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y−2/3, z+1/3; (v) x−y−2/3, x−4/3, −z+2/3; (vi) −x+y+2/3, −x+4/3, z+1/3; (vii) x−y+1/3, x−1/3, −z+2/3; (viii) −x+y−1/3, −x+1/3, z+1/3; (ix) y−2/3, −x+y−1/3, −z+2/3; (x) −y+2/3, x−y+1/3, z+1/3; (xi) x−4/3, y−2/3, z+1/3; (xii) −x+4/3, −y+2/3, −z+2/3; (xiii) y−1/3, −x+y+1/3, −z+1/3; (xiv) −y+1/3, x−y−1/3, z−1/3; (xv) x−y−1/3, x−2/3, −z+1/3; (xvi) −x+y+1/3, −x+2/3, z−1/3; (xvii) −x+2/3, −y+1/3, −z+1/3; (xviii) x−2/3, y−1/3, z−1/3; (xix) x−1/3, y−2/3, z−2/3; (xx) x+1/3, y+2/3, z−1/3; (xxi) x+2/3, y+1/3, z−2/3; (xxii) x−1/3, y+1/3, z−2/3; (xxiii) x+1/3, y−1/3, z−1/3; (xxiv) x+1, y+1, z; (xxv) x+2/3, y+1/3, z+1/3; (xxvi) x+4/3, y+2/3, z−1/3; (xxvii) x−1, y−1, z; (xxviii) −y+1, x−y, z; (xxix) −x+y, −x+1, z. |